I'm not providing specific product recommendations, because that kind of information goes out-of-date very quickly. (In fact, SE discourages shopping questions for that reason.) Instead, here are some tips on how to find what you're looking for.
Basically you need to find a camera that falls into two categories:
- Good for birdwatching.
- No monthly fee.
There are lots of guides for good video cameras for birdwatching; some provide tips on what to look for when shopping, while others are just comparisons of products currently on the market. I put a few links below. Eventually the information in these articles will go stale, but you can find more recent guides by googling for "best bird watching video cameras."
There are similar guides for home security cameras without monthly fees, eg this one: https://www.familyhandyman.com/list/10-best-home-security-devices-without-monthly-fees/
So what you need to do is look at both types of list until you find some camera options that fall into both categories.
Also look into trail cameras, which generally do not require a subscription (although many are designed to store video on an SD card rather than send it wirelessly, so you do have to shop for that). One of the bird watching guides recommended a camera from the CamPark brand: https://www.campark.net/collections/frontpage
My further advice is don't buy from Amazon or eBay or any of the generic online marketplaces, because they have a huge problem with knockoff products, so you really have no idea if what you're buying is actually the brand you think it is. Reputable brands with good warranties will not honor the warranty unless you buy from one of their official suppliers.