hdmi out port broken

First off, no - an HDMI to USB won’t work. Depending on the damage, you will need to replace the HDMI connector on the console which is a surface mount job. Much like the 360, the One does not turn on without a good HDMI connection and this has likely carried to the revised systems.

The guide needed for motherboard removal can be found here. Once you have the board out, see if it is something you need to send off to someone more capable or if you can handle it.

If the port looks okay, you will need to check the components around the connector and the HDMI IC. These can be damaged when HDMI is “hot plugged” without turning the device off unless the device is designed to do it safely (ex: laptops) unlike Composite and Component. The location varies based on the console revision you have (OG/S/X) but in general this is where it will be:

(One X?)

(One S)

The part number for the One S (based on the device selected; use common sense for the OG and X) is 75DP159. The One X being a 4K console will use a different part then the OG and S by the nature of the hardware upgrades.