This is a frequently heard complaint, but I can't imagine under what circumstances this would happen. I have hundreds of thousands of mails in tbird, in various accounts and folders. It's never struck me as slow. And its search (one of the features i use most) is simply fast.
I see it both fast and slow. Ironically it's absurdly slow on my 8-core desktop and just fine on my older dual core laptop (both with SSDs and same accounts, etc). Definitely weird, but this behaviour has peristed for years, so much that I had to disable TB features on my desktop just so I could type without stalling.
Might also recommend a disk check, perhaps FS needs fixing.
While helpful advice - if you need to do this manual maintenance regularly, the application is broken.
One day I'll finally take the plunge and jump to notmuch, which I've been told is the only email client actually capable of handling millions of emails without sucking.
The rendering corruption/lag issue with scrolling only happens while scrolling a message while in split-pane view, not when the message is maximized in its own tab.
Example: on two identical iMacs (4 cores, 16GB RAM, PCIe SSD) with about 100GB of local synced IMAP and the same accounts, it's slow for one user's iMac but fast on the other. Deleted TB and profile, fresh user, fresh TB install, fresh config; same result.