If you were only allowed to do three exercises at the gym to supplement running which would you pick?

Hex-bar Deadlifts (if you aren't maxing out, the last rep can also be a farmer's carry)
Parallel grip Chinups (with weight vest on some days, just bodyweight on others)
db Shoulder Press, or db Incline Press, or Standing Plyo-Overhead Press (~Jerk)

why would you go to a gym to do planks

Sounds like a terrible idea. You'd end up with one leg that was way stronger than the other.

I’d ignore the titular premise as silly and ask how many days a week and how much time per session would you be comfortable spending at the gym and towards what goal.

Dips, Squats, Pullups

Leg extensions don’t help your running at all. Good way to damage your knees though!

burpees

box jumps
weighted sled

Leg Press machine is trash for athletic development...

Front Squat

Trap Bar Deadlift

Bulgarian Split Squat

Alan

No it’s not trash, and yields a lot of the lower body strengthening benefits of free weight squats but just without the benefits of core stabilization.

This one made me laugh. Well played, sir/ma'am.

Nordictrac

Chuck Norris

7 minute abs

Haha good list! I’m partial to shake weight, LOL.

Still trash.

Front Squat, Back Squat, any squat...Zercher Squat? Bar behind the back old school Hack Squat.....all better than the leg press.

Alan

Seed and feed

Squats or Russian deadlift (power)

single leg RDLs (stability)

Hammer curls (upper body strength)

It's not just core stabilization it's everything stabilization. Leg press is also a higher injury risk for your back. The only reason to choose leg press over squats is if your shoulder can't handle heavy weights.

Back squat.

Hex bar deadlift.

Hip thrust.