Glad to hear your back is improving! Obvious "not a coach" caveats apply here, but I'm not convinced your strategy of skipping a workout to skip rope is the best plan. General recommendation usually seems to be to train to the best of your capabilities, whatever your pain tolerance allows without form degradation. Pain is complicated, and doesn't always mean you need to lay off. I'll let Dr. Baraki explain better than I can hope to.
Aches and Pains | Austin Baraki
TLDR; your back probably isn't in danger, and training through the perceived "threat" that squatting and deadlifting poses is probably the best way to get your brain to STFU about your back hurting.
Either way, jumping up and down hundreds of times (compressing your spine each time) probably isn't helpful.
Get back under that bar and get them gains!