Is there a source port with gameplay recording features?

Is there a source port that has a built-in ability to record gameplay? Or features that support it, like being able to enter a kind of flyby mode, where the camera goes around the level showcasing it? Or at least some way to quickly disable hud, weapon view, and let you manually steer around the level without the enemies noticing you?

Most Doom ports have demo recording.  Are you thinking about some other recording like a movie ?

Some ports have independent cameras, like Doom Legacy.

The ability to control the camera is limited, and not having used the camera to do things like you describe, I cannot say it can be done.

To me, it seems to require network play, with one non-player watching via the camera.   How to record that and what format you want, I don't know.

Play phobiata.wad with DoomLegacy.  When some keys are applied, a camera view flies around showing the application of the key to unlock something.

But, that camera is controlled by fragglescript and does not record anything.

No no, I mostly want to do a flyby through the level, so it's like invisibility mode + flying cheat + walking through walls + vertical look, all this with no hud. I want to record it as a video file.

Maybe,

If you wrote your flyby as a fragglescript function.  Put the fragglescript function into a PWAD.  Invoked the fragglescript function by a watcher.  Record the Doom screen using some OS application that can record an arbitrary window.

Maybe.

Easier if no other players need to be involved, just a passive fly through a level with a player just standing there.

You are going to have to read alot of docs just to see what various ports have to offer.

Huh, that's comlplicated. All I really need is freelook / free movement, something like the visual mode in Doom Builder, but in the game.

prboom-plus has support for all of this. You can bind a key to enable free camera movement during demo playback. Or you can use idclip, notarget, and iddqd cheat codes in the normal mode.

Use GZDoom. You can open up the console with tilde and type the following commands:
 

screenblocks 12
r_drawplayersprites 0
crosshair 0
noclip2
notarget

To break it down:

Screenblocks is the main hud. Setting it to 12 is essentially 'no hud'. To reset this, set it to 10.

r_drawplayersprites is the weapon sprite display. Setting this to 0 disables it. Setting it to 1 re-enables it.

crosshair is, you guessed it, the crosshair. If you don't have one enabled you won't need to turn this off, but 0 is the off setting should you want to disable it.

noclip2 (don't put a space before the 2) is essentially a better version of noclip, which also allows flight.

notarget stops enemies from targetting you (though they still will attack if you harm them)

As for recording the footage, I'd advise recording with software such as OBS.

Lastly, if you wanted to record some slow-motion footage, you could modify the game's timescale with:

i_timescale 1.0

i_timescale by default is set to 1.0. It acts as a multiplier, so if you want the game to run at half speed, drop that to 0.5. Want it to run double speed? 2.0.

Good luck. :)

Thank you both! That's awesome.