Hey! Just had a look at your photos and you're right, it doesn’t look like traditional stucco. From what you’ve described (and how it flexes), it’s likely an old elastomeric or textured acrylic coating, which was sometimes used to bridge small cracks and give that rough, stucco-like finish without being true cement render.

These coatings age over time, especially if they weren’t applied properly over a prepped surface. That’s why you're seeing peeling and cracking now, moisture might’ve gotten behind the coating, or UV has degraded it.

Here’s what I’d suggest:

1. Test a Small Section First
Before you go full power-wash mode, test a small area. If it peels off with modest pressure, you're dealing with a failing surface layer — but be careful not to force water behind siding or shingles.

2. Scrape + Brush Thoroughly
After power washing the loose stuff, follow up with a wire brush or paint scraper. For stubborn bits, a paint stripper designed for elastomeric/acrylics could help — just make sure it’s safe for outdoor use.

3. Check for Underlying Damage
Once clean, check that there’s no rotting wood, rusted metal lath, or water damage underneath — especially around trims and shake shingles.

4. Prime Well
Use a high-bond primer suitable for flexible or chalky surfaces. Some brands have primers designed for recoating over elastomeric or textured finishes — these help lock down edges and prevent future peeling.

5. Recoat Thoughtfully
Textured coatings like Bestcoat or Dulux Texture can work well, just make sure they’re designed for exterior use and are compatible with your primer. Apply in the right conditions (not too hot/cold), and follow cure times strictly.

It’s definitely fixable, but the key is prep, prep, prep. If it’s not sound underneath, any new coating will eventually fail too. If you're after more ideas on fixing wall surfaces,this post covers wall repair tips and product recommendations.

Hope that helps!