Party sync was a bit different before the level squish and has been a bit complicated by Chromie time, as well. Essentially, 50-60 characters in party sync will be temporarily synced down to 50, but will still gain XP if eligible. You are for all intents and purposes synced and the “same” level in BFA content which scales from 10-50. You will both gain XP in this mode (unless you are 60).
The sync will put everyone in the state of the character with the least amount completed in a zone. If you sync with a person who has done more quests than you, they will be temporarily locked out of quests you haven’t done but CAN replay all quests in the zone with you and gain XP until you’ve caught up to their spot and then their quests will unlock. Vice versa, if you have done all the quests in that zone, you would sync to whatever quest they are on and be able to replay it. Granted, if they are in the middle of a quest, it may be best to sync after they have completed and turned in that one, as sometimes it can be a bit clunky picking up the right quests in the right places. Whenever one person logs out, the syncing is removed and the person who has already done them has them removed from their log, so be sure the person recompleting the quests turns in any quests if they would like to gain XP. The resyncing can occur at every session, however, just something to keep in mind, so it’s not a big deal typically.
If you are in any other zone than BFA, and one character is level 50, it becomes more complicated because of the scaling of the zones. You can no longer activate Chromie time at level 50 and above, which scales all old zones to 50. You’d be in two different phases, like having war mode on and war mode off. BFA is the best place to party sync for leveling because of the scaling of the zone. Other zones you’d have to hop around a good bit to level in XP-appropriate zones.
And, yes, that BFA intro quest has been bugged for a little while. I have a bug report you can contribute to. Hopefully it will get fixed eventually.
I love party sync and think it was a great addition for areas where someone wants to help with a quest that involves phasing, or gain XP outside of Shadowlands beyond 50, but Shadowlands has muddied up some things with it making it a bit more confusing initially.