This guide uses Windows.

Install the following:
Foobar: https://www.foobar2000.org/download
Foobar's Youtube Source component: https://fy.3dyd.com/download/ (Preferences -> Components -> Install)
VB-Cable: https://vb-audio.com/Cable/index.htm

IF WINDOWS 10:
Settings -> Privacy -> Microphone -> Allow access to the microphone on this device = On & Allow apps to access your microphone = On

Microphone (if any) as the default recording device (disconnect when micspamming).
VB-Cable (CABLE INPUT) as the secondary recording device (takes priority when microphone is disconnected).
Foobar output into CABLE INPUT.
Steam overlay audio settings to take and output to the default audio devices.
Autoexec micspam command on the 5 keypad key.
Identical command on the mouse3 key to open mic without voice loopback (to voice chat instead of micspam). (This will mess up Mouse3 use for stuff like medshield on MvM).
To play music just open foobar, play music and press the 5 key to activate the micspam command. Press it again to disable the micspam.
To voicechat enable mic, press the mouse3 and speak. Press it again to disable the voicechat. 
(Optional) Change the hotkeys to whatever suits you better.
(Optional) Tweak autoexec configs to suit your tastes.
(Optional) Remove the default microphone button (default on 'M')

Only issue with this setup is that you can't micspam and speak/sing simultaneously, but you can fix that by patching both your mic and foobar into Voicemeeter Banana then patching VB into CABLE INPUT. For more details check this guide: https://gamebanana.com/tuts/14382 (Windows) or this guide https://web.archive.org/web/20220723134636/https://gamebanana.com/tuts/14757 (Linux)

Paste the following onto your autoexec.cfg file, located on SteamLibrary\steamapps\common\Team Fortress 2\tf\cfg\overrides if you are using Mastercomfig and SteamLibrary\steamapps\common\Team Fortress 2\tf\cfg if you aren't (you should).

//This one is for micspam
alias vtoggle "von"
alias von "+voicerecord; voice_loopback 1; alias vtoggle voff"
alias voff "-voicerecord; voice_loopback 0; alias vtoggle von"
bind KP_5 "vtoggle"
//This one is for voice chat
alias vtogglea "vonalt"
alias vonalt "+voicerecord; alias vtogglea voffalt"
alias voffalt "-voicerecord; alias vtogglea vonalt"
bind MOUSE3 "vtogglea"
//This is max volume
voice_maxgain 3
//Higher scale is louder but less quality
voice_scale "1"
//How loud is the music compared to the sound effects
voice_overdrive 5