I think 'stuff' is all very person dependant.
I am 35 weeks now, and haven't bought half of whats of the lists above, but have bought different stuff.
Baby bath - haven't bought, planning to just use sink or actual bath
Breast pump/sterliser etc - haven't bought. Have bought 1 emergency bottle and 4 ready made formulas incase needed. Otherwise plan to breastfeed and buy anything else as needed.
I have bought a pram, but right now it seems slightly OTT seeing as we can't go anywhere, so Baby sling will prob be fine the first few months.
Clothes wise, well baby due beginning May here, but have just bought some sleepsuits and vests, plus couple of cardigans. I figure if its cold they can wear vest, sleepsuit and cardigan. If hot then just vest. Or a combo of each. I would say for August the same would work. I have just bought some multipacks from M and S, they deliver (well do so far), and the quality seems good for the money. All the sleepsuits under 6 months have fold over mittens also. Ps the size 0-3 are big though with them, I had to order some newborn as well as when they arrived 0-3 was actually from 13lbs. Not an issue though as will fit at some point.
I think in the current circumstances certain items might take longer to arrive, but at 20 weeks you do have quite a while for things to change so wouldn't worry too much. The following would cover all basics:
- somewhere they can sleep and bedding
- car seat - need to get home
- some simple clothes
The rest really are nice and handy to have ie baby bouncer or muslin clothes, but if they can't be sourced alternatives are fine ie blanket on floor they can lay on, and an old towel cut up.
Actually one thing I am glad we have bought is reusable nappies. Disposables are currently not always easy to get, and I'm not sure how the situation will be in upcoming months as many made in asian factories. So maybe worth researching them anyway to see what your alternative options might be. But for me right now its one less worry of 'if' thye might be a supply source this summer. Same with formula tbh hence I would like to breastfeed if possible.
Sorry...essay length.