You're right, and here's how Twitter tracking works.

https://twitter.com/randomusername/status/1769420176942017694?t=XiPJOEOqQQ-C0aAmcNViDia&s=19

Not exactly sure what the 's=' stands for but may indicate which web browser or client the Tweet was copied from (assuming one uses the Share button to copy link).

I use a browser extension called ClearURLs which actually removes the 't=' variable from the link automatically but leaves the 's=' alone. Don't think it means much on its own.