Any advantage to purchase train tickets Bath to/from Salisbury in advance?

Question 1- Traditionally on this route there were only walk up fares. Then just over a month ago dynamic pricing, or Advance Fares to use the proper name, were introduced.
They are exact time dependent.
Given all you say I don't think it works for you. A normal walk up day return sounds the best fare for you.

Question 2- Yes, there is an ongoing risk of train strikes. They will be announced with 14 days notice, but timetables are only issued 3 to 4 days ahead. There is a strike mandate until the autumn (or fall).
So yes, you need a Plan B.
You can do the journey by public bus changing at Warminster but it is not time efficient, taking the better part of 3 hours each way.
If this day is a weekend there is the chance of a line closure, when trains will.be replaced with a dedicated express bus.
8 weeks notice should be given of that happening.

There are advance fares and on most mid August days you can get Advance £5.00 singles at present. Walk up returns are sitting at £22.10 for Monday. So there's £12.10 in it. So there is a small advantage in advance buying.

Train strikes are possible still but there will be at least 14 days notice of a strike. Exact routes get confirmed five ish days before, typically a Monday for a weekend strike. Chances of this being prioritised as a route is fairly low and if there is a service it's just luck as to whether it suits your plans

Thanks for the information and updates about strike notifications.
We are planning this day trip to Salisbury to be on a Saturday.

If we were to pre-purchase tickets (maybe assuming a 7:42pm departure from Salisbury), what is the best website to book from?

We were in Bath this spring and went to Salisbury for a day. We booked our trip to Salisbury ahead of time for a specific train time since we knew we had to be there with enough time to walk to the cathedral for our tower tour. We had the off peak same day return tickets and I looked up what trains that day we could use our return tickets for and we had no issues. I booked via the Great Western Railway website.

A Saturday changes the ticket complexion a little as that brings you into Off Peak territory on the day. But you will still find the £5.00 Advances if you get in early enough. If you don't want to be tied to a particular time to return then an Off Peak return will be fine.

If you want to get Advance fares you can buy your tickets from any of the UK train operators - this route is GWR (Great Western Railway) but you don't have to buy from them. Their website is one that often has issues, especially for non-UK users.

As well as all the train operators there is also the officially linked Trainline - they do charge small fees (they are removing these, not sure if they have on this route) but do have a superb app.

For Americans LNER tends to be the best website for buying train tickets for any operator.
Train line is not "officially linked".
They are a third parth consolidator.
The confusion arises from the fact that many train operators use Train line to fulfil their on line ticket purchases. Buying through a train company means that you do not pay fees and are dealing direct.
We know that on each strike day so far there has been no service on this route.

Thank you to everyone for their responses!

For only £5 each way, I took the risk and booked advanced returns thru LNER.

I selected the 7:42pm to Bath figuring we can either have a long leisurely dinner in Salisbury or we can go to Evensong in the Cathedral and then get a quick pub dinner before the train.

I’ll keep an eye out for any strike notifications in advance, and I’ll have an idea of what a car service might cost if I need to pivot as a plan B.