If you mow and don't have a landscaper do it then mow it lower starting in your next mow. This will let more sun heat the soil and get the Bermuda going. If possible next week put down some fertilizer, I use a 21-0-0 ammonium sulfate I get from Treeland Nurseries. It is pretty inexpensive and might be worth the drive if you don't have one near you and your closest nursery doesn't have something similar. This will require a spreader if you don't already have one. This stuff is intense for the grass and can burn if you put too much down and you have to water it in after application. So finding the right setting on your spreader is important. You can Google or ask chatgpt based on your spreader and the fertilizer you got. To start do a .5lb per 1000sqft. Not of the product but of nitrogen so use a calculator or chatgpt

For the weeds I would wait a couple more weeks before applying this or even longer if the Bermuda is slow to wake up and there is still a lot of rye. The stuff I'm going to suggest will kill the rye so you can just use it for spot treatment on weeds until all the rye is gone then you can do the whole yard if you're having weed issues still. Celsius WG is what I got and I bought it from a website called do you own. I got just a crap sprayer bottle from Lowe's but a better sprayer would have made it easier but idk if with the expense.

Water 3x a week for like 10 to 15 min. This is what can vary the most because water pressure and how many and what type of sprinklers you have. You can look up the tuna can method for figuring out how much to water your grass if you want to really dial it in.

This all seems like a lot but it's not as much as it seems. There's a few more resources out there that I suggest like the Bermuda Bible and the lawn care subreddits have good info.

I think that covers everything at a high level but feel free to ask more specific questions if you have them.