Great start.
You can progress faster. Much faster. Go straight to 100 in ten sets of ten. Do them every day and take as long as you want - all day if you like. You're going for overall totals to build the amount of work done; quantity, not necessarily intensity. Quantity you can do every day (think of it like a job); intensity requires rest. Consider the following rep patterns:
10 x 10
5 x 20
4 x 25
30, 25, 20, 15, 10
1, 2, 3, ... 9, 10, 9, 8, ... 3, 2, 1
Etc. There are many ways to hit 100.
Every now and again push yourself and see how many you can do in a single unbroken set (no pauses). Or see how many you can do with pauses (but still staying in position). Or see how quickly you can do 100 using any means necessary (sprinting, resting, gasping, crying, pushing again). Sixty in two minutes in a good total for anybody. Seventy is very good.
In 2013 I did 100 every day for the entire year. Some days I did more. One day I did 1000 (10 reps every minute, on the minute, for 1h40min). I did a total of 50,000 across the year. I'm 48 now and I don't think my body could take it but when I was 41 it could. Like you though, I started again while in lockdown. I've been using this app for the past four months and yesterday I hit 105 in one set.
https://play.google.com/store/apps/details?id=com.shvagerfm.Pushups&hl=en_GB
Well done so far though, you're made great progress. They really are an incredible exercise for all-round fitness.
So stop counting and let this app do the counting for you. Its better to breathe with ease rather than holding it to your next count or whatsoever. Just breathe normal and let the app help. https://play.google.com/store/apps/details?id=com.northpark.pushups
Im doing a pushup challenge every month and this was helpful.