John Dow

The engine version used to be shown in the past, however, with the introduction of LiveGrid and pico updates the engine updates became less important which is why the product version is displayed in the tool tip in current versions. Needless to say that decisions about changes in gui are made after deep analysis in cooperation of several departments and it's not just a decision of a concrete person.

... but was never implemented.
 
When I hover my mouse over the ESET icon on taskbar I get "ESET NOD32 16.1.14.0" . This is useless info, whoever installed ESET on their computer knows already that icon is for ESET ; additionally the version is not something we can double-check easily so again , without value .
Wouldn't be more valuable something like "Last updated 53min ago"   ???

It's up to our partners whether they'll offer 2 or 3 year licenses. It's likely that more countries will stop offering 3-year licenses this year.

ESET NOD32 Antivirus, ESET Internet Security and ESET Smart Security Premium version 16.1.14 have been released and are available for download.
Changelog:
Version 16.1.14
NEW: Added Live Tiles on Overview page
NEW: Added new Light / Dark mode switch to GUI
IMPROVED: Additional network details displayed under Network adapters in GUI
FIXED: various fixes and minor improvements
Known issues:
N/A
Upgrade to Latest Version
Upgrade my ESET Windows home product to the latest version
If your ESET security product has not updated automatically yet, you can enforce product update by manually checking for update in the Update panel or wait until it updates automatically.
Support Resources
ESET provides support in the form of Online Help (user guides), fully localized application and Online Help, online Knowledgebase, and applicable to your region, chat, email or phone support.
Online Help (user guides) Visit www.eset.com/contact to email ESET technical support

I don't know what detection you got. I got an alert about JS/Adware.Agent.AU when clicking an ad on their website. The detection is correct.

V16.1 is now available for download at https://forum.eset.com/files/category/3-early-access/.

Since subscription is currently used in the US only, please contact ESET LLC if there's something unclear regarding it. As far as I know, it's yearly subscription and can be de/activated in e-store after logging in.
At this stage when integration of the subscription system is still being worked on and decisions are being made, I'm unable to provide any further details. In the end, the system should bring benefits to users and make renewal seamless and hassle-free.

To my best knowledge, subscription is currently available only in the US. In the future, it will be available in all countries and the products as well as the ESET HOME portal will be better adapted to it.
If you don't need to share or otherwise manage your license(s) and do not use Anti-Theft nor Parental Control, you don't need to sign up for ESET HOME now.

I don't understand what is "ESET HOME" for.
I can perfectly read what EAV says and is in the screenshot posted below, but I can simply "see and manage" my (only one) EAV license in "ESET - Official Online Store" ( https://buy.eset.com/it/cart/login )
I can see when it expires, and how many (... one) I have.
So why open a new "account" or register in another (maybe useless, I don't know) site? 
I can't find anywhere what is the content of "ESET HOME", maybe I lost the right knowledge base page dealing with it.
Can someone post some screenshots to see what's inside? So that I can appreciate the difference?

ESET NOD32 Antivirus, ESET Internet Security and ESET Smart Security Premium version 16.0.26 have been released and are available to download.
Changelog:
Version 16.0.26
FIXED: Various issues and crashes with email clients and 3rd party plugins FIXED: Incorrectly displayed customized logo FIXED: GUI crashes Known issues:
N/A
Upgrade to Latest Version
Upgrade my ESET Windows home product to the latest version
If your ESET security product has not updated automatically yet, you can enforce product update by manually checking for update in the Update panel or wait until it updates automatically.
Support Resources
ESET provides support in the form of Online Help (user guides), fully localized application and Online Help, online Knowledgebase, and applicable to your region, chat, email or phone support.
Online Help (user guides) Visit www.eset.com/contact to email ESET technical support

ESET HOME enables you to manage your licenses or subscriptions as well as devices with ESET products. It also provides quick access to Anti-Theft, Parental Control and Password Manager for those who have ESET Smart Security Premium or ESET Mobile Security or Parental Control for Android.
With the transition to the subscription model it will gain on importance. In the future you should have just one account to ESET HOME and you won't need to have another login to e-store. As for activation, you don't need to know your license key, just connect your ESET product with ESET HOME to activate the license.
You can also install the ESET HOME app on Android and get notifications and warnings from the desktop security product, e.g. if you installed ESET on another family member's device.

Also of note is I have Firefox set to use HTTPS connection by default.
Eset does not block access to https://depositfiles.com/.

This statement needs further clarification;
Browsers have options to block pop-ups.
Pop-up ads although a nuisance are not necessarily malicious.
Browsers have extension/add-ons that will block ads.
Whether JavaScript code being processed by a browser is obfuscated per se is immaterial. It is only material if the JavaScript code after being de-obfuscated is determined to contain malicious code. Therefore in this instance, did the JavaScript code contain malware or perform activities that are suspicious enough to warrant blocking of the URL?

Correct. I'd only add that blacklisting a url takes only about 5 minutes until it takes effect in VirusTotal. In this case the url is not blacklisted but the JavaScript is detected when the actual html code is scanned. Scanning a URL at VirusTotal doesn't scan actual html content on the website unlike Quttera does and only compares the url with vendors' url blacklists.

There's an obfuscated JS on the website which is detected and is most likely responsible for pop-up advertisements:

That's because on VirusTotal you check if a website is blacklisted by AV vendors while AVs scan the actual html code to determine if it's malicious.

It should be reported to the developers of System Informer. What matters is that Explorer shows 1 (egui) or 2 (ekrn.exe) certificates as valid. One of the certificates is self-signed, hence the verification fails in Explorer too, however, this is perfectly ok.

I checked binaries on my installation and they have two certificates. One is OK but the other gives this error:

 
It seems that it's self signed and root certificate is not installed:
 

ESET still performs "classic" updates; OP is right, and info like "Last update performed on ...." is more valuable than "engine version".
"Engine version" is not posted on national TV , so we are aware of.....

That's great Staying with an Operating System that receives updates on regular basis (supported) is much better than using one that got left out of support.

In fact I got rid of Windows 7 and passed without any cost to Windows 10.
Remember that upgrading from Windows 7 to Windows 10 is still freely available online, and you can choose to keep your existing programs/documents at the beginning of the installation phase.
https://www.microsoft.com/en-us/software-download/windows10
In case one has problems with "Media creation tool", you can download Windows 10 ISO following this simple procedure
https://winbuzzer.com/2021/03/19/how-to-download-the-lastest-windows-10-iso-without-the-media-creation-tool-xcxwbt/
 

You are looking at wrong settings. In the advanced setup navigate to Notifications -> Desktop notifications -> Edit.

It was removed years ago. Now in the era of cloud and streamed updates, the engine version number doesn't matter much and the product version number is more important to show.

You can only filter out informative records or errors to hide those:

You should be able to disable the status in the Application statuses setup. V16.0 is the last version for Windows 7 / Windows 8.x, future versions will not support these older Windows systems due to signing requirements by Microsoft.