Have you enabled the autoupdate within the container?
If not please restart the container then it should update (my containers update the game on every start/restart of the container through SteamCMD), mine, with the auto update enabled, did the update about 8 hours ago.
Here is the part from the log where it updated:
UPDATE CHECK: ---New version of Valheim found, restarting and updating server in 10 seconds---
---Checking if UID: 99 matches user---
usermod: no changes
---Checking if GID: 100 matches user---
usermod: no changes
---Setting umask to 000---
---Checking for optional scripts---
---No optional script found, continuing---
---Starting...---
---Update SteamCMD---
Redirecting stderr to '/serverdata/serverfiles/Steam/logs/stderr.txt'
[ 0%] Checking for available updates...
[----] Verifying installation...
Steam Console Client (c) Valve Corporation
-- type 'quit' to exit --
Loading Steam API...OK.
Connecting anonymously to Steam Public...Logged in OK
Waiting for user info...OK
---Update Server---
Redirecting stderr to '/serverdata/serverfiles/Steam/logs/stderr.txt'
[ 0%] Checking for available updates...
[----] Verifying installation...
Steam Console Client (c) Valve Corporation
-- type 'quit' to exit --
Loading Steam API...OK.
Connecting anonymously to Steam Public...Logged in OK
Waiting for user info...OK
Update state (0x3) reconfiguring, progress: 0.00 (0 / 0)
Update state (0x1) running, progress: 0.00 (0 / 0)
Warning: failed to init SDL thread priority manager: SDL not found
Update state (0x61) downloading, progress: 98.05 (795715936 / 811503124)
Success! App '896660' fully installed.
And here a screenshot: