Okay, I figured it out.
Your compiler settings in TrenchBroom should look something like this (final compilation preset).

Run Tool

Run Tool

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Copy Files

Run Tool:

i.ibb.co/Y79DTkZ/setting.png
i.ibb.co/XtG4w4d/sly.png
Edited 11.76 hours after the original posting.

@NocturnalCult - I use Linux so the following will be different for Windows, but should be enough to give you the options needed.

Only parts of the compile script have been included.

buildBase () {
$Q3MAP2 -game quake3 -fs_basepath $GAMEPATH -v -meta ${MAPBASE}${MAP}
}
buildBaseSampleSize4 () {
$Q3MAP2 -game quake3 -fs_basepath $GAMEPATH -meta -samplesize 4 ${MAPBASE}${MAP}
}
buildVisFast () {
$Q3MAP2 -game quake3 -fs_basepath $GAMEPATH -v -vis -fast -saveprt ${MAPBASE}${MAP}
}
buildLightFast () {
$Q3MAP2 -game quake3 -fs_basepath $GAMEPATH -v -light -fast -patchshadows ${MAPBASE}${MAP}
}
buildLightFinal () {
$Q3MAP2 -game quake3 -fs_basepath $GAMEPATH -light -fast -patchshadows -samples 3 -samplesize 4 -bounce 8 -dirty -gamma 2 -compensate 4 ${MAPBASE}${MAP}
}
buildVis () {
$Q3MAP2 -game quake3 -fs_basepath $GAMEPATH -vis -saveprt ${MAPBASE}${MAP}
}
buildSunOnly () {
$Q3MAP2 -game quake3 -fs_basepath $GAMEPATH -light -sunonly -fast -patchshadows -samples 3 -bounce 8 -dirty -gamma 2 -compensate 4 ${MAPBASE}${MAP}
}
buildBots () {
$BSPC -optimize -forcesidesvisible -bsp2aas ${MAPBASE}${MAP}.bsp
}

To make a full, final build, the script would call:

buildBaseSampleSize4
buildVis
buildLightFinal
buildBots

A few links with a lot more details - en.wikibooks.org/w/index.php - and - openarena.fandom.c...g_and_packaging

A little note

Trenchbroom doesn't fully support the Q3 map format properly currently but does compensate with a Valve220 variant (which has more robust texture coordinates mainly). The NetRadiant Custom fork of Q3map2 should support this format

And regarding lighting, Your Mileage may vary. Experiment a lot with that, because Q3MAP2 enhances some and breaks some and doesn't reproduce Q3MAP's light rendering by default. Also the lighting may vary with engines and operating systems (i.e. linux breaking color ramps, sourceports breaking overbrights, lightmap normalization, etc.)
Edited 11.33 minutes after the original posting.

I promote the idea that people should stop using the built in compile options and just run a .bat file with the settings you want. Then you never really need to consider the level editor.

This is an example of the current one I use. These settings are the one I compiled Rustgrad with. What it does is that you specify a folder where the map is (like if it's inside "test" in the maps folder, just type test), then the map name and then the amount of bounces. It will output a log file where the compiler is located of it all.

@Echo off
Echo Map folder:
set /p Input3=
Echo Name of .map file:
set /p Input=
Echo Bounce these many times:
set /p Input2=
Echo Reticulating splines...

del "..\baseq3\maps\%Input3%\%Input%.bsp"
del "..\baseq3\maps\%Input3%\%Input%.srf"
del "..\baseq3\maps\%Input3%\%Input%.prt"
timeout /t 2 /NOBREAK > nul

Echo Compile began: >%Input%.log
date /t >>%Input%.log
time /t >>%Input%.log
Echo. >>%Input%.log
Echo ---- START BSP ---- >>%Input%.log
Echo. >>%Input%.log
"q3map2.exe" -bsp -meta -samplesize 16 -v "..\baseq3\maps\%Input3%\%Input%.map" >>%Input%.log
Echo. >>%Input%.log
Echo ---- END BSP ---- >>%Input%.log
Echo. >>%Input%.log
Echo. >>%Input%.log
Echo. >>%Input%.log
Echo ---- START VIS ---- >>%Input%.log
Echo. >>%Input%.log
"q3map2.exe" -vis -v -saveprt "..\baseq3\maps\%Input3%\%Input%" >>%Input%.log
Echo. >>%Input%.log
Echo ---- END VIS ---- >>%Input%.log
Echo. >>%Input%.log
Echo. >>%Input%.log
Echo. >>%Input%.log
Echo ---- START RAD ---- >>%Input%.log
Echo. >>%Input%.log
"q3map2.exe" -light -patchshadows -fast -samples 6 -gamma 2.5 -compensate 3 -v -bounce %Input2% "..\baseq3\maps\%Input3%\%Input%" >>%Input%.log
Echo. >>%Input%.log
Echo ---- END RAD ---- >>%Input%.log
Echo. >>%Input%.log
Echo Level compiled at: >>%Input%.log
date /t >>%Input%.log
time /t >>%Input%.log

Edited 11.39 days after the original posting.