By "non-financial assets" do you mean things like aircraft, yachts, paintings, property, etc. as in non-financial products that hold a monetary £££ account balance? aka fixed assets?
I think we all expect UK property ownership to be of HMRC interest and Land Registry are a feeder to DCDM. I can give you another example within the UK. CAA's Aircraft Register database lists the owner(s) of every UK registered aircraft. On a regular basis (use your imagination) CAA feed data to DCDM for every change in ownership, aka buyers and sellers. Let's say this chap, Joe Bloggs, is now the registered owner of a £2m Lear jet. DCDM will add this to his financial wealth footprint and some background calculations will be done. The simple outcome (there are many, but let's keep this simple) is that DCDM will confirm that Mr Bloggs had alternative wealth that aligned to a £2m aircraft purchase. If not, a risk is raised on the system that Mr Bloggs either used undeclared income or was gifted the aircraft. On the other side of the ledger (the seller) DCDM will check that the receipt of the £2m is reflected in that persons footprint. If lose ends emerge there is potential for investigation.
Anything else of significant value is shared in a similar way within the UK. Veteran and vintage cars are tracked via DVLA V5 registered keepers, changes will be fed to DCDM. I think there is a similar thing in the artworld for very expensive paintings. You can use your imagination to think of other assets that fall in to a similar style of high value.
Every single financial institution in the UK feeds regular data to DCDM - they create a footprint of the overview of your wealth, for everyone, but likely only 1% of the population are likely to have a tax yield gap of significance to interest HMRC. But the 1% membership changes as does the Bar-height for HMRC to trigger investigations.
As for outside of the UK, I'm not privy (above my security clearance) on the detailed content of the data that comes in to HMRC via the reciprocal Tax Treaty countries but I would not be surprised if it is massively different to the type of data in DCDM. Sure some less administratively advanced countries may be less diligent, but if I owned e.g. a property elsewhere in the world (there will be some exceptions obviously) I'd be fairly certain HMRC would know about it even if I haven't told them myself.
Regarding nations sharing info I recall this one from 20 years ago so predating ‘your’ system.
A businessman owned a well known restaurant i.e. a cash business. The French authorities informed HMRC that he’d bought an investment residence there with no borrowing. He then lied to HMRC that it was paid for by a loan/gift from someone in Italy. HMRC checked that with the Italian authorities, it was baseless.
Restauranteur was then taxed on the value as if undeclared takings, plus penalties and interest.
Even after all that he’d look professionals in eye and proclaim his innocence.