Perhaps try logging into your RCMP IWS portal to check the status. That will at least tell you if it has been processed.
My original PAL in 2006 I got from mailing out to receiving the card in about 2.5 months. That was in 2006.
My last PAL renewal in 2018 or so took 10 months...and that was a renewal (there were extenuating circumstances with them contacting my ex).
Given how innundated the CFC is with transfers nowadays and very likely new many new applications, my expectation would be at least six months...
I just finished my restricted course two days ago. After getting my papers back from FSESO in 4-6 weeks from now, I will mail my application out for my restricted endorsement (prob in early October). I am honestly not expecting to get my new card until next summer at the earliest, if at all (who knows what the government is up to). There's another fella that did the same as me (got PAL long time ago, just recently completed restricted) - he sent his application out in the winter and he still has not received his upgraded PAL yet. I would temper expectations for a much longer wait than 6 weeks.