Good response OP. You're going to smash this. The below is long but I hope helpful. I've worked in a lot of multicultural environments where people have very different levels of the 'official' language.
If it was my comment on paying more for being bilingual, I think the core thing is there shouldn't be a scenario where you are heavily dependent on unofficial translators. If the level of English is so low that translation is needed, it's not just about whether it's 'fair' they do this without reward - you need to have something more official in place and just because someone is bilingual doesn't mean that they're the right person to be doing that. There needs to some form of training, a process on how it will work and an agreement on what needs to be communicated in what language, and how you'll make sure that the right information is actually being communicated. Paying people more can be a part of that but it's actually a tiny part. Ultimately there is a large amount of trust placed in the translators here, and you can't just assume it is being done right. Eg if you say that an employee needs to work a certain shift, rely on a translator to get that message across, the employee doesn't turn up and says they were told the wrong information but the translator says that's not true, what do you do? Happens even if everyone speaks English but the language issues adds an additional level of complication that you need to work through.
It's hard to know from 'store' whether you're closer to the toilet cleaner scenario (where in reality customers do not have the expectation of material support in English), a large supermarket with high volumes of staff in warehouse roles and there are a large number of roles where customer interaction is similarly minimal, or a coffee shop situation where pretty much every staff member is going to have significant 1 on 1 customer interaction. In all of these it's important that there are official translations of critical information employees must understand (safety, data protection, confidentiality), including training. There's been a recent inquest where it was admitted that employees of a major coffee shop again would have had key allergy training in English only, allowed to take multiple credits and it was accepted they might need to rely on Google translate for some words.
Finally, you can't force someone to improve their English if they refuse to but you need to work out a way to upskill the people who are willing to learn because ultimately you want the best people in the more senior roles, not just people who happen to have been in the UK longer.
I'm working on the assumption that in reality you can't actually require fluent English for the roles because you won't have enough people who qualify who want the jobs and meet other key requirements. But even in the Bulgarian cleaning example, the cleaners are limited by their lack of English: I'll bet the manager speaks good English because there will be an expectation they can communicate on material issues and contract management in English. The company is also impacted (eg the safety / allergen labels on products will be in English so changing cleaning products is more complicated than it would be). Plus you set everything up based on Bulgarian and you might find you're in a position where good Bulgarian becomes a requirement for the role, and an influx of (eg) Romanian speakers to the area leaves you in a mess because you're not able to hire the best possible staff without redoing everything in a other language.
Dignity at work is very important, but core to that is ensuring that the workplace environment is set up so people can thrive. Inclusion comes from what people actually do, not the words they say. Not suggesting you think otherwise but I think in your original post you went down a rabbit hole.
If you're not going to require a high level of English to do the role, then you need to ensure that people who don't have good English can still perform well (and are supported in progressing in their careers if that's what they want).
And honestly I would learn the language but be careful to understand dynamics before you start using it. There's a difference between a customer learning hello in Bulgarian to be friendly, and a new manager coming in and immediately doing something to highlight that they're different to most of their team. In some teams it would work well, but if there is feeling that head office gives preference to Brits over the dominant nationality, it could make things worse and be taken as patronising. You don't know what you're stepping into initially so I would avoid until you know how it will go down.
Investing in learning the language will definitely be useful for you in the long term but it's clearly not something easy like French or you wouldn't be having the English language issues in the first place. That said, you may well find that in a year of two of learning (depending on language) you learn enough to know if someone is mistranslating or being disrespectful (to you or others) and people being aware of that goes a long way to stopping it happening. But of course, this could mean you spend years learning Bulgarian to find that demographics have changed, most Bulgarian speakers you're hiring are second generation now and so speak fluent English, and the people coming in are French speakers from Cameroon! I doubt you'll regret trying though.