Hi I usually lurk but I wanted to share my experience of doing this with you. The negative and positive. I'm self employed and with my first in 2019 I thought 8 weeks mat leave would be plenty (especially as I'd taken 2 weeks before the baby arrived) as I was only eligible for Maternity Allowance (came to about £140 a week at the time, here).
I ended up with quite bad PND and PNOCD because the people I worked with didn't understand how demanding it was to WFH with a baby and expected me to keep up with my previous workload, reply to emails as fast, etc, I felt all this pressure to keep earning, and I was being pulled in two directions (work and baby) and terrified of losing my income. I was setting my own hours and mostly working after DH took the baby to bed at 9pm but there were aspects of my job I just couldn't do at all due to baby brain/exhaustion (I wasn't even finding time to eat food some days).
I was recovering from a rough C section and had no family nearby to help care for the baby, and I was breastfeeding (and he had undiagnosed tongue tie and very bad reflux). These all played a part in how hard it was.
My best advice to you would be to see if you can find a way to take the financial hit to have even one more month on SMP. By 3 months, you'll have recovered a lot better, you'll have got into your groove a bit more with the baby, and you'll be familiar with their sleeping/feeding patterns etc.
By three and a half months PP, I was able to do long-distance drives from Ireland to the UK and attend business conferences (with my baby) and take in info and network, along with getting back to some semblance of normality. Work wasn't as smooth as pre-baby, of course, and the drives required a lie-flat carseat and lots of stops for feeds. A whole lot changes in both you and your baby between 8 weeks and 4 months, and in my opinion every extra week you can give yourself between then will set you up for a smoother return to work and smoother first year as a parent.
I'm about to have baby 2 (am 38 weeks pregnant), and I've organized a load of my work in advance to try and mitigate things a bit this time, along with freezing a load of batch cooks of my fave dinners, so PM me if you want to keep in touch for mutual support. I'm planning on going easier on myself and doing the bare minimum work to keep my business afloat this time because there were so many plates to spin. I hope that doesn't sound too negative because it's possible but really, really hard and I didn't manage it very well last time.
Before anyone on this thread demands why did I have a baby at a bad time, I want to point out it took 7 years to conceive my first (5 MCs) and we didn't expect to get PG on first try with our second.