Roof: Fascia board, which material? No gable roof overhang

Hello,

I have a question regarding a personal matter
What do you recommend for the fascia board at the roof edge as cladding?

We are getting a "modern" gable roof (30°) without an overhang.
The roof tiles will probably be a flat Braas Turmalin in anthracite matte, with verge tiles (half and whole) at the edge. The house will be brick-faced.

The builder has planned a wooden fascia board at the verge and behind the gutter on the eaves side.
The gutter is external, so in front of the facing bricks / clinker.

Since I do not want to paint the fascia wood, I am looking for durable alternatives.

[*]Wood: Must be painted
[*]Zinc cladding (the fascia board is extensively clad with zinc sheet): Expensive (the general contractor wants a €4,700 (I) additional cost. That is too much - especially since the zinc sheet also starts to rust at the cut edges.
[*]Aluminum, stainless steel? More durable in terms of material, probably even more expensive
[*]Plastic profiles instead of wooden board: Seems good and inexpensive. Not my visual favorite, but okay. The general contractor is now obtaining a quote for that.

Have I overlooked anything?
Should a protective screen against insects (wasps) and birds also be ordered?
Thanks for your input.

Slate, roof tiles with verge nose, copper.

Flat roofs also have no roof overhang...

Copper does not fit into the concept and budget.
Roof tiles have an edge fold of about 6 cm over the verge.

Attached is a section of the roof edge.

What I wonder is whether the wooden board can be omitted with the zinc cladding? So just metal, without having to elaborate on covering the board.
Zinc verge flashing actually doesn't cost much, about 7-8 EUR per meter.
You can't reach the executing roofer yet through the general contractor, but I will follow up on that.

I got the insect mesh idea from the green forum; it was about small animals, wasps, swallows, etc.
The mesh is not necessary, but it seemed plausible to me, although I have nothing against swallows at least.