Is there an advantage to using one - 36V 50AH deep cycle lithium battery instead of three -12V 50 AH deep cycle lithium batteries? Other than the obvious space savings?

Weight savings. A much flatter power curve. Faster recharge. But….when it dies, it dies.

I don't think you can jump start your big motor off the 36V. Also if one of the 12V batteries were to fail you could stick a regular wet cell in there in a pinch.

You’ll also need a 36v charger

I use 3 50ah batteries. I have the force trolling motor. If one happens to [censored] out I can still use two batteries 24v without a hitch. I have Noco charger 4 bank charger.

Easier to weight balance with the 3 separate, I switched from a single

As mentioned, a little more flexibility with 3 12v batteries but there is no capacity advantage.

12v @50ah = 600 watt-hour
600 watt-hour x 3 batteries = 1,800 watt-hour

36v @ 50ah = 1,800watt-hour

I have 3x 50ah batteries on troller
Like stated above I don't know if there is any advantages other than charger options..
Jump starting is a possibility that way but still have to be mindfull, most lithiums (once shut down from low voltage) should be waken up based on manufacturers recommendations.. I have jumped mine with no issues, but some manufacturers have preferred methods
Also keep in mind if you kill your cranking battery and trolling batteries to the point they shut off your dead on all accounts.. there is no dwindle down voltage to look at graphs, run lights, power pole down, or even trim motor
I only bring this up because I recently had an alternator issue and ended up standing in the water for a couple hrs waiting for a friend to come tow me in

On a related note, what is preference to Prismatic or Cylindrical cells? Been looking at a few companies and of course each is best and better than the other, etc... Hard to make a decision without knowing what is real and what is salesmanship, etc...

From what I have been able to research...
Prismatic is newer tech, able to be smaller/lighter for a given ah rating, less internal connections required (less welds), slightly less power capacity, better for motion use (ie cars, boats, etc), with 10 year warranty BUT pro-rated after 5 years.

Cylindrical is older tech, a bit larger and heavier for a given ah rating, more internal connections/welds, slightly better power capacity, better for stationary use, with 10 year warranty, not pro rated But cost about 25-50% more depending on size

Most probably know the two brands I am describing above, but wanted to leave brand name out as I was more interested in thoughts on the technology differences...

If I was going to build the perfect scenario boat battery set up.
I would go with a 36V battery for my 36V Ultrexx trolling motor. I currently have 3 12V, but if one of them goes down you are just as you would be if you had a 36V battery go down.
I would also put in a 24V battery for my Garman with Livescope. (24V captures a much better uncluttered image. And once you get below 11 volts the Livesocpe won't work.)
and then I would put a 12V gel cell battery for my motor.
The problem with this scenario and this is probably the reason that will make your decision to just stay all 12V batteries is - you would have to have a 12V battery charger for the starting motor, a 24V charger for the Livescope, and a 36V charger for the Ultrex.
that is unless someone makes a charger that can charge various voltages, while they do make chargers that can charge lithium, gel cell, and lead acid, I don't think you can get that set up, plus different voltages, so this kind of explains why your probably better off with 3 12V lithium's, otherwise you're going to have multiple chargers.

So don't be a dumb [censored] like me - make sure your charger has the capability to charge lithium's for your trolling motor and whatever else you use for your motor. I went lithium 2 years ago and had a 2006 Ranger charger and and in 6 months I screwed up one of my batteries. Called tech support and they asked what type of charger i had and sure enough that battery charger wasn't rated for lithium and was the issue. I could see thru blue tooth on my phone my batteries were not getting fully charged and finally over time one battery bit the bucket. I asked if it was under warranty and of course he said no, but he did walk me thru on how to jump start that one battery back to life and it worked and everything has been running smooth for 18 months now.

same here except I have the minn kota precision 4 bank

I run the Impulse Lithium 36v-40ah with the charge on the run charger. I've fished all day tourneys and still have plenty of power remaining, this is the system https://www.impulselithium.com/product/36v-40ah-platinum-series-dc-charge-combo/