After confirming your health is fine take a step back a bit. With your first baby coming in a month go enjoy some outside riding now and focus on having fun.
Once you have a baby getting away for an outdoor ride will be hard- even an hour by yourself on the trainer will be hard.
I have memories of putting my first born in one of those swings and lulling him to sleep, then setting him up besides myself in the trainer. If he started stirring I would reach down and rock him. Sometimes I could get in 30 min…
Having two kids who are now 7 and 10 I would advise simply trying to find time to exercise enough for mental health when you can and do your best but the reality is the baby is gonna take up a lot of time and energy.