Staffing issues are partly a knock-on effect of lockdown and resulting inflation. Benefits sanctions were suspended once lockdowns started, but never properly restarted (the civil service presumably doesn't much enjoy sanctioning people). So for a lot of people, they are getting free money without the obligations to seek work that previously went along with it, and benefits/pensions have also been pinned to inflation whereas private sector wages aren't. It adds up to strong incentives not to restart work again.
Sounds like they're not paying their staff enough. If they're not having trouble with staffing on busy nights, but are on quiet ones thats a pretty sure sign that they need to raise their pay. On busy nights staff might be okay with the lower pay thanks to tips, but otherwise its likely more profitable for them to go work somewhere else that pays better.
It's more likely that on quiet nights/days it's simply not cost effective to open. During a weekday a small pub might literally have one or two customers. They're traditionally owner-operated for a reason, and the reason is because the margins don't allow for staff.
Definitely changing that though, esp over last 10 years. Many pubs in London (and increasingly other areas) will put an "optional" 12.5% for service for food, especially if they have a "dining area" off the main bar. It's also increasingly common for pubs to have people asking if you'd like another drink, and charging you 12.5% for the pleasure - this seems to be a lingering effect after covid where you couldn't go to the bar to order.
At least when food comes into it they may do, quite a lot of tips where my brother worked a few years back (pooled and shared between bar & kitchen staff). Nothing like the US though indeed.
It might not be applicable to the UK, as someone else pointed out, but this is absolutely the case in the US. On a good night, a server might make several times more than their hourly wages in tips alone. I've known plenty of people that worked as wait staff at a restaurant that liked the tipping system because thanks to tipping their wages were several times higher than minimum wage. Most of them would have rather had a slow night once in a while rather than give up the tipping because of how much they made thanks to tipping.
However, they all have staffing problems, and some have to close part of the week because staff presumably find better work elsewhere.
Couple that with sometimes extortionate business rates and many average pubs in remote areas are simply not viable.