I come bring myself to buy a set of (nearly!) £200 wellies, partly because I won’t get a huge amount of use out of them i reckon.
However I do want some waterproof boots of some sort.

I’m going to start back outdoor climbing later this year, when my little girls is abit older. I’m thinking something like a tall lace up boot with a tongue that is apart of the shoe, not loose, maybe like a tall waterproof approach shoe

Does such thing exist?

Quite a few approach shoes / trail shoes come in a mid version. My inov8 roclite come in a shoe and mid, the 345 gtx something or others have a tongue that’s part of the whole boot. also something like scarpa zodiac comes in a shoe and a boot version.

neither are like wellies tho

If I’ve got the jist of what you are after maybe something like this?

Kamik Canuck

More for winter snow and ice than mud really (though I wear them on short muddy walks instead of walking boots because my wellies are not too comfy) and I’d not walk up a mountain in them but they are my outdoor boot of choice when knocked about outside the house in the winter doing jobs (nice and warm when v cold in the workshop or doing outside jobs) or short walks in for winter dunks in the river (not in the river obvs – walking to and from).