advance purchase ticket, two carriers, what if first train is delayed and miss the 2nd?

If it's a single ticket you can take a later train to York.

The allowance given for the connection by Underground between the two stations is normally very generous so with a slight delay with the first train you should have plenty of time.
If its a longer delay you should get your ticket endorsed at the barrier at Paddington or ticket office and then best go to the ticket office at Kings Cross to explain the position

Ps the cost of the Underground between the to terminals should be included in the cost of the ticket

if you booked it yourself as two unrelated tickets plus the tube it is your responsibility to get to the second train on time.

As said above, if it is one ticket, no hassle no problem.

If you do get one ticket it will expect you to use the tube as part of the journey and will print a little cross or dagger in the lower left of the ticket - that means that the trip on the tube is included. You wouldn't need a seperate tube ticket. Since I don't trust ticket barriers to always return the ticket I often go to the staffed gate and show the ticket without putting it in the machine.

I'm interested that you are making two sides of a right triangle. Future readers may wish to consider travelling on the hypotenuse - via Bristol and Birmingham on the Cross Country line.

If you do have two distinct tickets to and from London you are still covered for travelling on the next service in the event of a delay if one of them is also valid for a Zone 1 underground journey. You aren't if they are both to London Terminals and you pay for the connection separately. Any decent retailer should cover this.

Also if you are delayed for 15 minutes or more don't forget to apply for delay-repay.

if you booked it yourself as two unrelated tickets plus the tube it is your responsibility to get to the second train on time. As said above, if it is one ticket, no hassle no problem.

As per much of the advice on the forum I used https://www.nationalrail.co.uk/ instead of a reseller to find the tickets, although National Rail then forwarded me to London North Eastern Railway (LNER) from whom I purchased the entire journey.

If you do get one ticket it will expect you to use the tube as part of the journey and will print a little cross or dagger in the lower left of the ticket - that means that the trip on the tube is included. You wouldn't need a seperate tube ticket. Since I don't trust ticket barriers to always return the ticket I often go to the staffed gate and show the ticket without putting it in the machine.

Thanks for the tip, I didn't realize that! The email confirmation does show 3 journeys including that leg, but I had figured it was my responsibility to get between stations.

I'm interested that you are making two sides of a right triangle. Future readers may wish to consider travelling on the hypotenuse - via Bristol and Birmingham on the Cross Country line

It surprised me too, but the National Rail site shows the more direct routing via Bristol as taking 5h35m and the one thru London as about 4 hours.

Thanks to everyone for the help. I know there's a million things that can happen on a trip and nobody can plan for all of them, but I also can envision myself as a flustered tourist standing in Kings Cross who missed his train and wonders what happens next.

but I also can envision myself as a flustered tourist standing in
Kings Cross who missed his train and wonders what happens next.

In that case, just board the next train to York and look for a seat that isn't reserved.