Is there a big difference in riding comfort between a 700x32 and a 700x35 tyre? As a beginner would I notice a difference?

I doubt you would notice a difference. We are talking about only a 10 percent wider tire. Many other factors such as tyre pressure and the terrain you ride on come into play - any tyre is comfortable on a perfectly smooth surface.

There was a video by Path Less Pedaled on Youtube where he said that 40mm tires did so the trick on cobblestone. But I would say in my opinion choices like 700x40mm or 27.5x2.00 are the more comfortable choices. Or I'd go minimum 38mm. By the way, the Vittoria Randonneur in 40c is actually 36mm (even the Panaracer Pasela 700x38 is 36mm).

3mm, not much difference. Advertised vs actual measured width of a given tire can vary more than that sometimes. What sort of terrain will you be riding?

90% payment and 10% bike paths

Trekkin I have 700x25s on my 2006 Felt F65, 700x28s on my 1984 Nishiki international and 700x35s on my Charge Plug road bike (not an e-bike), and 26x2.125 smoothies (54mm) on my drop-bar Blazer MTB. I ride mostly pavement, and keep the tires firm-ish...not rock-hard, but not soft.

In a straight line there is not much difference to be felt, except for braking. The wider the tire, the better the rear tire grabs to help slow and stop the bike...although that may also have to do with overall weight.

When cornering, the wider tires grip better and instill more confidence for faster turns with more lean. I already had 1.85" smoothies on my MTB when I converted it to drop-bars and the cornering was exquisite. The 2.125 Finccis are just a little heavy and a little less cushy than the 1.85 WTB Slicks which don't seem to come in the 26" size anymore.

As far as comfort...

The fatter slicks on the MTB win. With so much tire volume, it is easy to run them at a lower psi, and get a cushy ride with more grip. Even running them firm as I do, they provide a cushioning the thinner tires don't.

The 35's also have an easier to find sweet spot where there is firm responsiveness and an occasionally noticeable cushioning.

The 28s and 25s are either firm and responsive, or too soft. It is too difficult to find that sweet spot.

It also bears mentioning the frames...my lightest bike, the Felt is aluminum with carbon chain and seat stays, a carbon seat post and carbon cranks. The frame itself absorbs some shocks and is more comfortable than just aluminum. The 1984 Nishiki International's frame is a skinny steel affair, very flexible with very thin seat and chain stays seat and a long, thin curved front fork. It provides a lovely ride, even when I first got it and it had 700x23s on it. In that case it was the rear grip in braking and overall stability that led me to put 28s on it. The frames of my Charge Plug and Blazer are steel, but rigid enough that almost all of cushioning comes from the tires...although the Blazer has a seat with springs, left over from when it had straight bar and I sat a little more upright. It really only comes into play when there is an unexpected pothole.

And that reminds me that since I ride on the hoods in a road position, it is easy to lift off the seat and relax my legs and arms to help soak up identifiable bumps. Since I mostly commute along familiar routes and know where many of the bumps are I can anticipate them.

I'll also mention my two folding bikes...a 2005 Dahon Boardwalk with 20x1.5s and a 1989 Dahon Getaway V with 16x 1.75. I put bull-bars on the Boardwalk for a very road-bike like position. The smaller Getaway still has straight-bars and a very cramped cockpit, although I still manage a "hunched-over" position. These bikes have rigid frames (the rescued Getaway still a little rickety). on both bikes, the super long seat posts provide a little cushioning, as do the wide-ish tires, which also give good grip for cornering and braking. For what it's worth I don't feel any difference between the tires on those bike with regard to width, although the Boardwalk has much better Schwalbe Marathon Racers which grip well and have supple sidewalls.

I don't know what my conclusions are but these are my observances.

Thanks
The 700x32 tire is on the 2023 FX3 model and the 700x35 is on the 2024 Trek FX3 model. Just don't if it's worth waiting for the 2024 model to be released
I know that I can upgrade to a wider tire but I would want to wear the original tires out first

You might see a bigger difference between two different tire models. Particularly between the budget tire and a high dollar tire.

this: high end tires make a huge difference, a high end 32 will be smoother than a lowend 35.

I was amazed at the difference when I first found this out years ago

As others have noted, a tire with a supple casing can have a significant effect. But those who say "no difference you can feel" on 35 vs 32 mm, the 35 will have 20% more tire volume, and so can be run at significantly lower pressure which will have a bigf effect on comfort. See: https://www.renehersecycles.com/tire...re-calculator/

No good reason to wear out a set of tires that you don't like. They aren't that expensive. I would upgrade and keep the old tires - many uses for them. I felt like a sad sack once when I had to go the bike shop and ask for a replacement for my blown out tire. They didn't care, but I felt small for admitting that I didn't bother to keep any spares on hand. Also, what if the shop was closed?

Also interesting that you use the word "upgrade". Perhaps an upgrade, but tire width is certainly debatable.

Another big consideration is rim width. If 32mm is close to the limit for the rim, then 35mm can feel squirrely. OTOH on a wider rim the same 35mm tire will feel great.