You provide very limited information.
What do u mean by managing 1k accounts on web.telegram.org? do u want to do things manually or use something like playwright? Manually managing 1k accounts is crazy.
I really really don't understand what you want to do.
The web telegram application is fully opensource, but more important: the MTPROTO protocol is as well.
You don't need to manage with the web app, you can just create a program imitating official APIs.
So u don't need to use things like Playwright/Puppeteer, and it would add a terrible overheard, and be slow as fuck.
If u want to access some of the accounts manually, u just need to convert the 1k accounts session you bought to ur provider, to the session format the web app is using, and it
is not really hard to do as this application is opensource:
https://github.com/TelegramOrg/Telegram-web-k
Finally, the telegram account won't "die off", if its used for another account? Do u mean if its used by another session?
No, you won't be disconnected if another session is connected to ur account, and if u mean "if 2 connections are made on the same session", then yeah, you'll get the following error:
So I think you are searching for something to register session automatically to Telegram web.
Well, you just need to do what I said earlier, reverse engineer the way Telegram Web K is storing sessions(its simple, u need to find how does it store the DC ID(optionally its address and port, but this can be found with dcOptions request), and the auth_key_id). With these two things, you can basically connect to any account, with any clients: you will need to extract that from your current session and then inject it to the web app, where it stores it.