Monitor connected via HDMI freezes and disappears when connecting a Thunderbolt to DP monitor on MacBook Pro

that dell S2421HN display appears to be a full HD 1920 by 1080 display with 8 bits/color Millions of colors

Interfaces

• 2 x HDMI (HDCP 1.4)

This one could easily be supported on the direct HDMI port, PROVIDED you use are using:

HDMI cables you want for HDMI-only Displays (higher resolutions than 720p TV sets) are marked as Certified with an anti-counterfeiting tag and are labeled:

"PREMIUM High Speed HDMI cable" or that + "with Ethernet" (up to 4K at 30Hz) --OR--

“ULTRA High Speed HDMI cable" or that + "48G" (supports higher resolutions and backward-compatible)

Cables with No Certification tags are good for your standard 720p TV set, and not much more.

what make&model displays?

connected how, exactly? {separate cables of type ___ , through a USB dock, through a Thunderbolt dock, over Airplay, something else}

Typical default connection for an additional display is extended desktop, but it is possible that if you have previously mirrored these displays together, that could cause some problems.

that dell P2418D display appears to be a "2K" display 2560 by 1440 with 8 bits/color and top refresh rate for 60 Hz.

interfaces include

1x HDMI 1.4

1x DisplayPort 1.2

Your DisplayPort adapter is likely acting as a USB-C adapter, and still has lots of spare bandwidth.

But the cable/adapter or cable in use should be such that the USB-C section and the DisplayPort section should EACH individually be no more than ONE meter in length. Longer on either side of the adapter electronics can cause signal attenuation that leads to transmit errors, which will Shut Down the connection.