Here a better view of the rooflines.

This won’t help you with shelter from the rain (if that’s your goal), but if your goal is to give the entry some prominence, I’d think about a pergola extending fairly far forward. Painted white, with vines growing up and baskets hanging down, maybe a bench along the left, it could look quite inviting.

Could you extend that little roof over the ovalish window across to the other side? It would even out the roof line and not take a lot wood or shingles.

A nice awning in glass and metal would be good.

What does limited budget mean? Entry point for a portico or porch cover in my area is around $15k. With the roof and gutter work involved you're def north of that.

If you're in an area that gets snow I can't see an awning-type approach being a great idea.

I’m a single family income who has to diy because I don’t have 15k to invest in a beautiful addition. What I want and what I can afford are to different things. Lol champagne taste beer budget! Also, the glass awning I did myself to the back entry but that would never be approved on the front entry by the HOA. I need something to stop the rain from coming in when you open the door. It’s gets the collection that once you open the door like break the weather streaming seal it gushes in on you. It just need to protect the door from rain elements.

That suppose to say weather stripping seal. But the point is rain collect and if you open the door during the rain your dunked like a bucket of water. The gutters are cleaned out and working and even added another down spout hoping it would reduce the collection. The pitch roof leading directly to the front door doesn’t help the situation.

Birmingham Alabama prays for snow. We rarely see it.

Since you are in a HOA, drive around to locate the other houses that are the same model. Chances are good someone will have solved this problem already. You can use google streetview to "drive", too.

Do you know how much coverage you need? 6 inches, 12 inches, more? A small overhang painted the same color as the house or in white matching the trim would be quite unobtrusive, but if it needs to be 18 or 24 inches or larger, then the HOA will probably take more notice when you put in your proposal for approval. BTW, inviting the HOA board members over when it rains may help your case. Or make a video next time it rains.

I would be very upset if I had a house built and this was the builders solution for a front door. And in a neighborhood with an HOA? Shame on your builder...

Oh trust me, I am not happy about it. Like I said thought it was gutter issues but they’re fine. So plan B got a new door since after 10yrs it rotted out. Now plan C, protect the door from the rain. Just need so price and structure ideas

If you can't really change much due to HOA and budget do you just need something to keep rain off a little. I found this. A home improvement center might carry something (I hate to order things you are not sure of off internet) I saw some aluminum ones and some listed as clear so must be plastic and less than $30, but probably not long lasting as a aluminum one would be.

https://www.doorclosersusa.com/Aluminum-72-Rain-Drip-2-1-2-X-5-8-p/155a72.htm

What about taking the door out and setting back a bit to create a porch ?.if you have room for something like that .

I'm big into diy, but this isn't something I would do. It needs to look professional and like it belongs on the house (plus you don't want to run the risk of any unseen leaks causing wood rot)

Something like this won't interfere with the existing roof (yours would have to be lower, of course...) and looks good to my eye...