Had this in mind while watching again and spotted that the calendar under their anniversary photos says February 2022 during the flashback to their I don't love you anymore argument. Wen is clear there that in his mind they are already broken up. Alan seems to accept this at the time and agrees to be friends.
Their first anniversary was in May 2017 btw, so May 2022 would have been their sixth anniversary. There's no photo for that of course.
The majority of ep 5 takes place late December 2022. Jim and Wen meet 10 Sept 2022 (on Jim's beer). So at least six full months (March-August + ? weeks either side) between flashback argument and Wen and Jim sleeping together and 10 months between the flashback and Xmas arguments. Add in however long from initial breakup to flashback argument.
I didn't realise Wen had keep Alan in limbo for THAT long. My dear boy, what were you thinking? (Before this, I'd assumed the flashback argument was fairly recent.)
Getting this down whilst I have the dates fresh in mind. Will be back after I watch the rest. From what I remember of Alan and Jim's conversation re timing, I think there might be some internal inconsistency between the visual date and dialogue.
Re the ring - Alan is wearing a ring in the flashback to their 1st anniversary, which seems more like timing for couples rings. They were already living together. Alan certainly acts like he had made a long term commitment and assumed Wen had too. My main thought on this question is that the inability to register a marriage contributed to the messes between both Jim & Beam and Wen & Alan. Their respective situations might have come to a head sooner, and been resolved with less mess, if they'd had to decide whether or not to make formal legal commitments.