A full underside rustproofing treatment sounds like a good idea ,and those selling the service will certainly tell you it is . But its probably not going to be cheap.
I have only looked at one example , on the following website.I am not recommending it in any way. Others may be cheaper or better
https://www.rust.co.uk/product/half-day-rust-proofing-service-price-list/They sell the materials separately for diy but offer a service to treat the car. For the full treatment for a car the size of a Jazz, it costs £575 +vat, which in the real world means £690.

This includes (they say) removing loose underseal,plastic trays, spraying cavities, and treating any surface rust. it takes 2 days. They do offer partial treatments for less, but its still expensive. They dont offer any guarantee on cars over 3 years old and recommend some retreatment every 2 years
The film they use is called Norwegian Corrolan made with lanolin from sheeps wool. applied as a spray or a hot mist. Nice if you are a sheep but likely to be a washaway product imo.
But I would not have it done. At least not by professionals. I am all for treating rust as soon as it appears , or taking early action against stone chips etc. But cant help thinking £690 plus any subsequent treatments might be better spent on buying a newer car that much sooner. . Sell the old one whiles its stlll got some life left in it for the next owner.
I bought my first brand new car, a Nova, in 1984. I saw recently that good examples are now regarded as classics selling for £5000 + The Pam Ayres Poem "I wish i'd looked after me teeth" came to mind. But the reality would have been driving around in an increasingly older obsolete car for 30 years (or better still not driving it much) until it became a rarity.
Had I bought a brand new mark1 jazz in 2002 and spent lot of money keeping it pristine, I'd still be hankering for a fuel efficient and quiet Mk4 if my depleted funds allowed. . It would be someone else that would benefit from buying an old car thats rust free. I know some will be horrified at my attitude

Its a personal choice.