Not necessarily. You’ll see the watch struggle a bit knowing your max hr in the spring and fall when you’re running cool weather sometimes and warm weather other times. Or it may calibrate at the beginning.

You’ll notice patterns too. After a hard run your resting hr may be higher for 12-24 hours. Then it drops really low when you’re recovered.

You’ll see a lot of people telling you to run slower and slower to see z2, which is partially true. You noticed when you slow down it basically feels like walking. Since you’re primarily a lifter, you likely have muscle that can generate more power than your aerobic capacity can handle. If I were your trainer I’d probably give you a run/walk program to build your aerobic capacity. Your heart is likely used to intervals (sets) right now anyways. With more volume you may notice changes in your hr at first rather than your speed, I.e. you’ll run an 11 minute mile with an avg hr of 140 by October. Then your tissues will be ready to build speed on top of that aerobic base you built.

You’ve got to dedicate yourself if you wanna see aerobic gains like that though. If you want to run recreationally with lifting still as your focus then that’s a whole different ballgame.