How can I make my phone HDMI compatible

It's not going to be possible to actually add an HDMI port to an existing phone; there's no hardware inside to support it, nor is there software in the operating system to run it. You'd have to redesign the motherboard, modify the case and build a custom version of Android that includes the drivers needed for your HDMI controller chip you add to the circuit board. That's all fairly advanced electrical and software engineering skills; as one of those engineers it's not something even I'd try.

You can, however, buy an inexpensive USB-C to HDMI adapter that will do the job; they're running around $3-4 on AliExpress, and of course you can find them on lots of other sites like eBay and Amazon, among others. Here's just the first example that came up on a search.

4K 60Hz Type C to HDMI Adapter USB 3.1 HUB HDTV Converter Cable for iPhone 15 TV Converter for PC MacBook iPad Samsung Laptop - AliExpress 44

Note that this is not an endorsement of this part, just an example of what you're looking for. I've used a similar one on my Pixel phone and it worked fine, allowing me to connect my phone directly to my television.