Well done!
If this was my project, I would use a spar urethane but, thin it down by up to 50% with mineral spirits or paint thinner.
I happened to find this thread about a simple way to apply the finish that may help you also.
https://www.thewoodwhisperer.com/articles/a-better-way-to-apply-spar-urethane/
The polyurethane may amber over time but, since your project has a weathered look, I don't think it will matter at all.
Also, since the poly is thinned down so much, I don't think the amber will be as noticeable either.
Thanks for sharing and God Bless! Spirithorse