No Linux client. Use the browser dev console (F12) with the web apps.
Where Microsoft 365 / Office keeps its logs
Microsoft 365 / Office logs to %WINDIR%\Temp\ on Windows. 3 other Windows log locations are recorded below.
Microsoft 365 / Office logs to ~/Library/Containers/com.microsoft.errorreporting/Data/Library/Caches/DiagnosticReports/ on macOS. 1 other macOS log location is recorded below.
Paths are printed exactly as Microsoft 365 / Office writes them. Environment variables like %LOCALAPPDATA% and $XDG_STATE_HOME are never expanded, so a path can be pasted straight into a shell. Where a path differs between installer types or shipping flavours, each one is racked as its own card below - why that happens.