I haven’t seen anything like that. YET.
New(ish) Features Starting To Become Very Irritating!

Steven, you are absolutely right, these pop-ups are quite annoying and do not carry any useful information.
Moreover, they are even harmful, they steal our precious time, which is always in short supply 😼

For me, these popups normally only display once after I delete my browser cache. Or if I use a private or incognito window to log in when I'm not using my personal computer.
Stephen, have you lately deleted your cache or history? Otherwise, you shouldn't be seeing these; might be a bug.

Are you getting them also Ivan?
I used to see them quite often. I'm not a premium user, maybe because of this.
I hope my eyes never see them again 🙈

For me, these popups normally only display once after I delete my browser cache. Or if I use a private or incognito window to log in when I'm not using my personal computer.
Stephen, have you lately deleted your cache or history? Otherwise, you shouldn't be seeing these; might be a bug.
By coincidence I did clear my cache and all cookies (etc.) about a week ago but I've been seeing these pop-ups daily for ages. I'm not aware of a day when I don't get at least one.
More likely to be the cause is that I switch my router off every night before going to bed. I do that to avoid the small risk of fire from it over-heating and making sure no one hacks into it. I've wondered for a while if that's why it's happening because I get assigned a new IP address (I think) each morning when I switch it back on.
Although why a recognised member of the site should have to see those annoying boxes every time is beyond me. Beyond being yet another aspect of not well thought through design, I can't explain it.

I started noticing them all the time a few weeks ago. I click on Lessons and there's a popup explaining that Lessons are to teach me about chess. Well, duh. When I click puzzles, there's a similar popup explaining that puzzles are chess positions in which I should find the best move. Okay. Who thought of these time-wasters and why did anyone agree to it?

By coincidence I did clear my cache and all cookies (etc.) about a week ago but I've been seeing these pop-ups daily for ages. I'm not aware of a day when I don't get at least one.
More likely to be the cause is that I switch my router off every night before going to bed. I do that to avoid the small risk of fire from it over-heating and making sure no one hacks into it. I've wondered for a while if that's why it's happening because I get assigned a new IP address (I think) each morning when I switch it back on.
Although why a recognised member of the site should have to see those annoying boxes every time is beyond me. Beyond being yet another aspect of not well thought through design, I can't explain it.
It shouldn't be happening after a week of clearing your cache and cookies. I don't think it should be triggered by new IP addresses either because most ISPs utilise dynamic IPs for their clients anyway. I don''t see such popups even when I access the site over my VPN.
Perhaps, because many people are experiencing the same issue, it is a site-wide problem. Maybe try opening a ticket with staff now, I guess.
...
P.S. My router has been on a non-stop marathon since the day it landed in my home. I don't even know if the damn thing overheats. I also never worry about it being hacked -- not in my low-budget universe. Unlike Stephen over there, who I'm pretty sure has a secret stash of bitcoin that could rival a pirate's treasure chest!

I think some of the annoying notifications can be turned off by unchecking the automatic boxes for "Chess.com news and announcements" and "Lesson & Practice Reminders" if you go to https://www.chess.com/settings/notifications. I still receive some of the pop-ups, but less than I used to. Perhaps chess.com could implement a setting to block pop-ups on the site?
I can't remember exactly when this started but it was sometime in 2022. I suddenly found pop-up dialugue boxes where they hadn't appeared before. Here's an example of them from this mornings visit to chess.com:-
First I needed to check on the progress of a tournament in my club and before I'm allowed to do that I have to be shown this for some reason ....
I've been a premium member of this site for over ten years so why on earth do I need to even see that? What is it telling me that I didn't know years ago? Absolutely nothing, so I click to get rid of it.
Then I go to check on one of my vote-chess games and need to check out the move options in Explorer and gues what? ...
So why on earth do I need to see that? What is it telling me that I didn't know years ago? Absolutely nothing, so I click to get rid of it.
Finally I want to check the notes in one of my clubs and you'll never guess ...
Why on earth do I need to see that? What is it telling me that I didn't know years ago? Absolutely nothing, so I click to get rid of it.
I'm interested to know how many others are seeing these pointless boxes which serve only to stop me geting to the things I need to do. I challenged the staff many months ago in a report/complaint and asked if these boxes could be disabled (they appeared unrequested from nowhere, so you'd think they could be sent back there).
If I received a reply (I can't remember), it was something like 'it's done, live with it'.
Why must I be made to wade through irrelevant 'trash' (afaic) in order to get to the things I want and need to do on this site?