Will expats, resident in other countries, be given this new Brit ID??

Why should they?

Maybe if you're a British national and passport holder maybe you would be issued one?

Who knows at this point, not even Starmer I'd wager

Eta, following the news brief it appears to be a bit of a half hearted attempt and it's a work permit, no digital id no job.

But if you are one of those employers who employs people working under the table then the digital ID is irrelevant as you won't be asked to produce one.

Exactly, a diversion from Burnham?

But any employers now can't say, I wasn't aware

That very much depends on what it turns out to be in practice. At the moment it's being touted principally as a measure to tackle irregular immigration by making it obligatory to have one in order to work in the UK.

Leaving aside any discussion about whether it will be effective on that score, on that measure alone it ought to be available to non-resident UK citizens for the simple reason that we have the unconditional right to live and work in the UK, and can currently prove our entitlement by showing our passports. If it becomes contingent on another form of id, then we should have the right to acquire that. We wouldn't have to be habitually resident in the UK to want to exercise that right - some people might pop in and out of the country on an ad-hoc basis and pick up casual or temporary work when they're there.

Another matter on which there are currently obligatory checks, which will only be able to be performed with this id in future, is the right to rent property. For those of us who don't have 2nd homes in the UK, it's feasible that we might want to have a place at our disposal for longer than we'd want a holiday let, whether we intended to occupy it full time or just as and when over a given period.

If the longer term objective is for it to be used as authentication for most or all interactions with the state, that is another reason why we might not just want, but actively need to be issued with it. Many of us still have dealings with HMRC, for example and many more, I'm sure, with DWP.

Probably being a bit pedantic here but the Guardian quoted Lisa Nandy as saying :
Lisa Nandy insists digital ID 'will not be mandatory for people to use'

... which is contradictory to what was said elsewhere and therefore mightily confusing, but does she really mean UK citizens as in anybody with UK citizenship or as in everybody resident in the UK? The former would seem a bit of overkill as there are lots of UK citizens the world over, some of whom may never set foot in the UK.