Does the Macbook Pro 2019 13' Support Display port 1.4

https://www.apple.com/macbook-pro-13/specs/

Get help with video issues on external displays connected to your Mac - Apple Support
 https://support.apple.com/en-us/HT201177

Using 4K displays, 5K displays, and Ultra HD TVs with your Mac - Apple Support
 https://support.apple.com/en-us/HT206587

Use the LG UltraFine 5K Display with your Mac or iPad Pro https://support.apple.com/en-us/HT210205

You can use that adapter, but whether or not it will support the HDR option I cannot say, since I have not used that adapter. You'll have to try it out.

See here for HDR support on Macs: Play HDR video on your Mac - Apple Support

DP Alt mode is only required in USB-C connections on the receiving display that requires it. Macs don't support DP Alt mode at all over USB-C. But its not required to maintain 60hz when going to HDMI.

Since you are going to HDMI, there's no way to support DP Alt mode on it. HDMI does not support it. Its a USB-C option only.

However as shown by leroy above, the Mac can support 60hz output for 4K.

You will want to use this adapter for it: USB-C Digital AV Multiport Adapter - Apple to maintain the 60hz over HDMI.

This adapter allows you to mirror your Mac display to your HDMI-enabled TV or display.

3840x2160 at 60Hz on:

iPad Pro 11-inch, iPad Pro 12.9-inch (3rd Generation),

MacBook Pro (15-inch, 2017 and later), iMac (Retina 5K, 27-inch, 2017

and later), iMac (Retina 4K, 21.5-inch, 2017 and later), and iMac Pro

(2018)