My dog has eaten half of bottom of the fence post

Dig around the post and concrete a repair spur to the broken post bolt then both together and it should fine after that

I'd sleeve the eaten part with 25mm thick treated timber. Just before you put the last bit of sleeve on, by screwing them to the post, put some expanding foam in to fill the eaten part. If you need more detail, let me know.

Possibly install a new post as in time a repair job will still fail. Steel plates screwed or bolted in place to brace the missing wood, will only weaken the post further. Plus labour and materials. Old post out, new post in. Perhaps wrapped at the bottom with chicken mesh to prevent dog eating the new one. Hope this helps.