New wall mount needs 75mm drill depth. Would you be concerned about this in a brick party wall?

[big-all]

worth noting that some houses have brick features between on the outside that will replicate the wall thickness like corbels or brackets to the gutter or roof so look front and back
you can also off course measure wall to door or window frame edge from both sides and the difference is wall thickness

 

[Lucid]

On party wall thickness: You definitely can find houses with a one-brick-thick party wall. I know this because the first house I bought had exactly that.

This was a late 19th C Victorian terrace. I was chopping out for some additional power sockets. The brick went through to next door.

Regarding bracket fixing, I would either use some kind of plug or, where strength is definitely required, a resin and stud solution.

Expending solutions such as Rawl bolts are not good in brick. There's too great a risk of hitting a mortar joint or the edge of a brick which then fractures as the bolt collar expands. It is even possible to split a brick. All of these things compromise the anchorage.

Plastic plug sleeves provide a malleable joint boundary. This is kinder to the wall. Resin provides a large contact patch which fills an irregular shape effectively so long as the hole is dust free.