how reliable is UK's train system

You are overthinking it - there's a very low risk - trains are generally pretty reliable, and unless there's a catastrophic meltdown, there are multiple alternatives. We went through a period of strikes last year, and I traveled to the UK and took trains on five trips, and never had a problem.

There will never be an unexpected train strike - the unions have to give advance notice (two weeks off the top of my head). There's no current action pending or expected.

There's really nothing you can do to reduce the risk, except personally I never take a flight the same day as a train trip.

It's worth noting that they do tend to plan track maintenance on Sunday and bank holiday periods.

What journeys have you got planned?

There are never any unexpected train strikes. As for other eventualities well stuff happens. Engineering failures, cattle wandering onto tracks, fallen trees, suicides these all happen occasionally. I can only say that in 50 years of train travel in the UK I have never failed to reach my destination, even if the train company has had to pay for me to take a taxi (happened once).

That is simply not true. For one thing fourteen days notice has to be given of any strikes- unexpected train strikes simply cannot happen in the UK.

For a second thing,

if a late train is cancelled, you may end up without a place to stay for the night and risk losing prepaid hotel bookings, entrance tickets, or plans for the following day.

that will not happen. The railways have a legal duty of care to get you to your final destination that night, by whatever means is necessary. That may be by bus or by taxi (paid for by the railway), or by alternative rail route if one exists. That applies no matter what kind of rail ticket you have. In the past I have known a 3am taxi arranged from London Euston to Penzance where a connection for Paddington from Manchester to the west country sleeper was missed due to a very, very late train.

That will be arranged by rail staff.

Renting a car at the last minute in the majority of cases would be very hard as outside of airports most rental companies close for the night at 5 or 6pm.

Two examples-
a- When I am travelling back from London to home on the edge of the Lake District after 4.30pm I will always have a through ticket to my final destination, even if that costs me a few £ more than dividing the journey into two tickets. Thus my intentions are clear to rail staff. The 4.30pm gives me options and plenty of buffer time before my last train from Carlisle at 10.09 pm.
b- I live on the Cumbria Coast. The last train all the way down the coast (from Carlisle to Barrow) is at 7.09pm, although there are later ones until ten pm part way down to Whitehaven. Last night the 7.09pm to Barrow was cancelled as was the 8pm to Whitehaven, both due to staff shortages. So intending passengers were put on the 8.55pm to Whitehaven with a special connecting bus to Barrow at 10.15pm running all stations. It is only a 45 mile journey but knowing that road all too well and the diversions to remote stations they wouldn't have got to Barrow until well after midnight.
However people were also given the option of going on the WCML down to Lancaster, connecting there for Barrow. That probably got them to Barrow before the 7.09 train down the coast would have.
Also if disruption is announced early enough in the day then on all ticket types you can travel up to two hours early if that suits you.

I have been through my share of cancellations and delays. The latest this past Sunday on Scotrail. Enroute to Glasgow. We pull into Stirling station--the last stop before Glasgow--and sit for 50 minutes. Apparently, there was a signal problem ahead of us.

So my only advice is don't cut train times too short. If there is someplace you have to be on arrival, don't plan to arrive too close to that time. Give yourself some leeway.

The good news is...if your train is more than 30 minutes late, you can apply for delay compensation. I should get 50% of my fare returned. If the delay was more than an hour, you get a full refund. I'm still waiting to hear from Scotrail about mine.

I've never been stranded. The train company has always come through, one way or another, to get me to my destination. Sometimes rerouting, sometimes replacement buses.

The trains are very reliable. If you click the following link and put in today’s date (or yesterday) and select all day and the location(s) being places you intend to be travelling from/to, it will show you if the trains ran on time. (Note that those in faint type are freight trains). If you then click on a train, you will be able to see if it kept time on its journey.
https://www.realtimetrains.co.uk/search/detailed/

If you happen to be awake during British daytime and click the following link, you will see the position of all the passenger trains. All those in green are bang on schedule. Click on any one of them and its route will be shown. https://www.map.signalbox.io/[email protected],-2.16945,7Z

I have 2 examples of Frank II's tip that if you are delayed you get a partial full refund. Happened twice to us last fall. Not strikes, just trains running behind schedule. Once was a partial refund, but only London to Oxford, so it probably cost the railroad more in administrative costs than the value of the check. I must have paid for one of the tickets either in cash or missed the "always pay in dollars" advice. The small refund was in pounds and since the check was only 6.10, it would have cost me time and money to deposit it, so I didn't bother. The second was London to York. More than 1 hour late, so they refunded the entire cost of our tickets. The pricey one I got back in dollars.