This is happening to me as well. At first I thought that it was due to having multiple windows (since two times it stopped happening after I closed the second window) but it's still hapenning.
Sometimes it just constantly refreshes the page, others it refresh after some time (and somehow I lose my session). It doesn't seem to affect just one site.
Version 0.99.134-beta (WebKit 622.1.9.19.2)
Build date June 10, 2025
MacBook Pro (macOS Sequoia 15.5 build 24F74)
Edit: just tried with todoist.com and Version 0.99.133-beta (WebKit 621.1.2.111.4) and I'm experiencing the same refresh and session logout even with compatibility mode enabled.