Sounds like it might be the same issue reported here, given how unpredictable it is: steamwebhelper keeps crashing on startup · Issue #11262 · ValveSoftware/steam-for-linux · GitHub
If the issue does happen again, I would check your webhelper related logs and see if anything matches up from the report’s log on it.
I would suggest again to try disabling hardware webpage rendering and seeing if that does help if the issue does persist.
In Steam’s menu go to Steam > Settings > Interface and then disable the “Enable GPU accelerated rendering in web view” option. (It requires a restart of Steam to take effect)
Also try running it sometime not directly at startup. The reporter has a hunch that it might be some kind of race condition (so maybe it might be failing other checks too if ran early).