Sql-server – Why MSDB transaction log file grew while MSDB was in Simple recovery mode

In AGs writes can only occur on the primary. Shrink operations are writes. Therefore you must do the shrink on the primary. Note that the shrink may not shrink as much as you expect, your test on the restored DB had probably leveraged simple recovery model. Read How to shrink the SQL Server log for more info.

Do not shrink to 160MB. Determine why did the log grow to 121Gb so it does not repeat (you have a suspicion, would be nice to confirm if possible). Size the log to a size appropriate for your operational needs. Log growth is a serious problem, it cannot use instant file initialization and all your database activity will freeze while the log grows and is being 0-initialized. Users and apps hate it when it occurs. If you understand the impact and your users are OK, you can shrink once to a small amount (160MB is probably too small though) and let it grow until it stabilizes.

It is impossible for us to guess what is causing it, but SQL Server doesn't just grow a log file to 300 MB for the heck of it, it grows to 300 MB because at some point since your last shrink operation, it needed that much log space (whether due to some big single transaction or a lot of smaller concurrent ones). You'd have to trace log file growth events (I talked about this here and here) to try and narrow down when or why this happens (also if you log file growth setting is 300 MB or something, then it will grow by 300 MB as soon as it needs more than 1 MB of space to accommodate active transactions).

Anyway, why do you think you need to shrink the log file once it has reached 300 MB? Did you actually read all of the answers, thoroughly, on Mike's question? The log file is NOT going to shrink on its own, because shrinking the log file to 1MB - just so it can grow again during your largest transactions - is a total waste of time. What are you going to do with all of that free space in the meantime?