A skinsuit or roadsuit will definitely make you faster on the bike. It's pretty easy to measure the effect with a power meter.
Weirdly "aero socks" are both a thing and make a big difference to the point that they are heavily regulated by the UCI.
Any cylindrical part of the bike or rider is going to perform badly so if you can encourage the airflow to stay attached around it you reduce the amount of effort required to move you forward, hence aero clothing being a big deal.
If you're a serious cyclist then it's pretty easy to spend money on good quality clothing.
Always made me wonder if taking the swimmers route instead would provide all the same benefits without the cost and look. Shave your whole upper body and go shirtless and you would be pretty damn aero no? Would a skinsuit really improve upon that?
In addition after switching to a Brooks saddle (I tried literally 10s of saddles using the "saddle swap" forum feature on some forums) I now no longer ever want to use padded bike shorts again. Of all the short types the simple padded chamois was my favorite (simple foam - no gel or any other BS) and now I just prefer wearing a pair of synthetic lightweight boxer briefs (no fly) that were designed for hiking originally. There is no padding at all and from day one the brooks was extremely comfortable. It only got more comfortable with time and applies all pressure directly to my sit bones. Every other saddle + padded short (even ones that mostly were on my sit bones) ended up forcing padding into the areas between my sit bones and outside them as my weight compressed the padding. I havent tried their new non leather seats but they seem to operate by a similar tension (a tensioned pliable surface vs a hard plastic shape with padding on top) which results in your weight creating additional space below the sit bones vs filling it with padding.
It's actually been tested and modern fabrics are better than bare skin for drag.
In Michael Huchinson's Faster[1] it mentions that they tested a rider naked in a wind tunnel to find out!
If you look at a modern TT skinsuit you can see that they try to cover as much of the arms and legs as possible. They usually stop above the elbows and knees because it's hard to cover the joints without wrinkles.
Likewise, socks are now as long as permissible (without breaking the UCI sock rules!), which I think is about halfway up the calf. It would be faster to cover all the way up to the knee joint.
It all sounds silly if you don't race but if you've put some effort into getting fit then after awhile it's hard to gain even 5 or 10 more watts. If you can reduce your drag by more than that just by wearing a better pair of socks... well why would you?
BTW I have a Brookes on my commuter Brompton too. :D