I make a lot of stays built up of consecutive reservations. If you stay at a hotel in that way, my experience is that you receive one choice of bonvoy-related welcome gift at the start of the stay (points, breakfast etc), not at the start of each new reservation, as everyone is saying above.

Depending on the hotel, they may send a new helping of their own welcome gift to the room when each reservation changes over (eg. fruit bowl, snacks etc), but that is very much local policy dependent.

Whether your stay is made up of one reservation or five, your Bonvoy account will credit with one EQN for each night you stay at the hotel, and total points adding up to the total spend.

But, and this is what the OP may be referring to, in my experience each reservation will credit to your account separately as the stay progresses, when each reservation ends. My only experience of it not happening like that has been when I have either arrived on one reservation and then kept extending it directly with the front desk, or if I have asked the hotel to combine separate reservations on one folio and post it all at the end (but even that is not always foolproof).
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I don't think it really matters which way you do it, you receive the same points etc in the end. The only situation where I can think there might be an anomaly is if you were registered for a promo that awards bonus points after a certain number of stays. I'm guessing that reservations posting individually could potentially trick the system into awarding points in that scenario, but I have never been in that situation so have no experience either way. Technically though it would still only be one stay so those points could be taken back later.

It is quite handy sometimes to have very long stays posting in stages due to separate reservations, to gain access to the points. And on the occasions there have been posting issues and I have contacted both regular and Amb CS there has never been any pushback that I am still at the same hotel and will have to wait until I finally check out. And that's over a period of several years at multiple hotels in 4 continents. Just my experience so far though, YMMV of course.