Frances starting March 10, so via Valcosta as Napoleon is closed. I assume booking through to Pamplona should start soon given crowds and many albergues being closed for the winter?
There will not be crowds in the first half of March, but when you get to the period March 22-31 (Easter week and the adjacent weekends) the numbers will increase a lot - not just pilgrims, but many Spanish people travelling for the holiday week.
So, don't worry about the first 10 days of your Camino, unless you are super-specific with your accommodation requirements/expectations. Once you have walked a few days, you will get much more comfortable with anticipating your needs and preferences.
I recommend booking your place in SJPP in advance, so you feel better about showing up in a strange country and town, while jet-lagged. There is no panic for this, since there will not be big crowds on March 9-10, but it is nice to get that done. You
know that you'll need a bed in Valcarlos and Roncesvalles (unless you are confident you want to go further), so you might want to book them as well, whenever those bookings open up in 2024.
You will be arriving in Pamplona on a Thursday or Friday. Thursday will certainly be no problem, but you always need to be aware that weekends can get busy in popular cities. However, booking something in Pamplona in mid-March (i.e. before the Easter fortnight starts) could be done a day or two before.
Arriving in Burgos during Easter week (a great idea, by the way) could present a problem IF you need a private room, so you might want to work out which day you expect to arrive there, and reserve something. If you are willing to stay in an albergue, then you will probably not have a problem as the big albergue does not accept reservations, and the peak pilgrim traffic from SJPP does not happen until May.
For the rest of your journey, it depends on how tightly you want to commit yourself in advance and what your needs are. I think it would be fine to play it by ear (i.e. educated judgement rather than "winging it"), anticipating a few days in advance, and especially watching for where you will arrive on weekends. Even the famous Sarria to Santiago crowds should not be an issue in March-April. The facilities will be open for the season, and there is enough accommodation for the much larger crowds of July and August.