Hi Kate. I've taken a while to respond to this, hoping I might get my thoughts in order but it's going to be a bit of a brain dump instead. Sorry if it's hard to follow.
For context, I've ridden the Hebridean Way, B&Bing it. I have in-laws in Lewis who we visit regularly. My wife and I have been to Uist for our main holidays for the past seven years. My last job was supplying hire bikes and cyclist "taxi" services in the Scottish Highlands and I've been involved with hundreds of Hebridean Way cyclists as a result.
First of all, it's a fantastic trip. Regardless of the weather, folk come back buzzing about it. Many of our customers also highlighted just how friendly and accommodating the drivers were - even those who came from countries we'd otherwise think had better cycling infrastructure. Eight days is a decent amount of time. Too many folk rush through it (I did). When you allow for ferries etc, that time soon gets eaten up.
A Specialized hybrid will be fine. About half of our hire customers used those. The roads are pretty good and a slightly wider tyre will let you explore some of the machair path in South Uist - definitely worth a detour.
As already said, try not to take too much stuff. The steep hills aren't long and the long hills aren't steep, but I've seen lots of folk pedalling glumly as they are just overloaded. Do use all the gears - something many folk seem to avoid(?) A rack and panniers should be more than enough. If you have access to some small panniers (and the means to mount them) for the front then that can make the bike a bit more balanced. Many European cyclists actually prefer to have front and not rear panniers. a small handlebar bag of some sort is useful for keeping day-today items close at hand - money/cards, camera, phone, guide book etc. Something that can be quickly detached and re-attached will be great for cafe stops etc.
There are a number of good campsites. I especially recommend Kilbride on South Uist and Balranald in North Uist. Kilbride also has a hostel. Balranald is in the middle of an RSPB reserve and is next to a fantastic beach. There is a food van open during the day with fantastic scones, cake, soup and fresh crab rolls. I really can't recommend it highly enough.
If you are camping or B&Bing keep in mind that evening meals might need to be sourced elsewhere and not all B&Bs will have somewhere to eat close at hand. Do some research before you go to make sure you'll get fed. If you can, also pre-book your evening meals. The islands have got increasingly popular and restaurants/hotels are often fully booked in the evenings. In any case, always carry at least one days food with you. You should be able to top up each day but the gaps between shops can be quite long - and remember that almost everything will be closed on Sundays (many tearooms etc will still be open though - moreso in Uist than in Lewis/Harris on account of the religious differences).
Usually, you can just turn up at the Barra-Eriskay and Berneray-Harris ferries, but do check ahead. The past couple of years (as a result of Covid) even cyclists have needed to book.
Following NCN780 is your best option, though detouring onto the machair path for a few miles from Daliburgh northwards is a highlight. When you get to Harris you can either go up the Golden Road on the East side or NCN780 on the West side. I prefer the latter for its extensive beaches, views and a few more facilities.
My experience of the weather is that you'll either have a wet tailwind or a sunny headwind
Take Smidge and a midge net. It's usually to windy for the midge to be a big problem but when that drops they'll want to make up for lost feeding opportunities.
I assume you've looked at the logistics of getting to Barra and back from Lewis?
I'm sure I'll think of more stuff afterwards, at which point I'll post again. In the meantime, if you have questions about any of the above (or anything else I can help with) fire away.