How do you play videos from PC/laptop on TV screen? What are the best ways, wireless if possible?

I'm just plugged in with an hdmi.

If I'm on the go, I'll hook up my laptop to the TV with an HDMI cable, set the TV as a duplicate screen so I can close the lid on my laptop (make sure closing the lid doesn't lock your computer or put it to sleep), then use my wireless mouse and keyboard so I can sit on the couch/bed/whatever and control it from afar.

At home, I bought a micro PC that I keep connected to the TV via HDMI. Then I use a wireless mouse/keyboard to control it from the couch.

The micro PC has WiFi so I can connect it to the Internet, and all devices on my home network can see each other, so I can quickly copy something from my regular PC or laptop to the micro PC if I want to view it on the TV.

I mostly use the micro PC for my streaming services. I don't trust my Smart TV to be connected to the Internet, so I don't use any of its apps. But I'm old; I'm used to TVs being dumb devices. I don't like handing over control of my apps to companies; I'd rather access them directly from a computer.

wifi from a phone. hdmi from everything else

I use a Steam Link, but that's no longer available as hardware, only an app. I don't have any experience with it but I read somewhere you can set up RaspberyPi to work in the same way.

Though I have to say - while it works wirelessly, for games it is better to have wired connection.

I use Rygel on my laptop to serve all the videos and VLC for Android on my Chromecast which is connected via HDMI to the TV. Both Laptop and Chromecast are on the same WiFi at home.

You could try and bridge it with the steam link app.

I'd suggest figuring out the Windows casting issue. My TV is hardwired to the network, so maybe that helps.

Here's a script for a mode switcher. Works great using psexe to wrap it in an executable.

Do {
    CLS
    $Mode = Read-Host "`r`n(W)ork, (P)lay, (M)ovie?"
    } until ( 'w', 'p', 'm' -contains $Mode) 

if ($Mode -eq "w"){
# Work Mode
displayswitch.exe /extend
# Display taskbar and restart Explorer
$p='HKCU:SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\StuckRects3';$v=(Get-ItemProperty -Path $p).Settings;$v[8]=2;&Set-ItemProperty -Path $p -Name Settings -Value $v;&Stop-Process -f -ProcessName explorer
    }

if ($Mode -eq "p"){
# Play Mode
displayswitch.exe /external
# Display taskbar and restart Explorer
$p='HKCU:SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\StuckRects3';$v=(Get-ItemProperty -Path $p).Settings;$v[8]=2;&Set-ItemProperty -Path $p -Name Settings -Value $v;&Stop-Process -f -ProcessName explorer
    }

if ($Mode -eq "m"){
# Movie Mode
displayswitch.exe /internal
#Hide taskbar and restart Explorer
$p='HKCU:SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\StuckRects3';$v=(Get-ItemProperty -Path $p).Settings;$v[8]=3;&Set-ItemProperty -Path $p -Name Settings -Value $v;&Stop-Process -f -ProcessName explorer
    }

I use an HDMI switch to connect my computer and my chromecast to my projector since it only has one HDMI in port. Wireless comes with all sorts of possibilities for signal degradation (interference mainly, especially from wireless controllers or any smarthome stuff you may have).

Try a file app that allows you to view local network devices. If not, with a little more configuration you can find out about Kodi or Plex

I used to have a Miracast dongle and it worked like a champ. No wifi needed and it did exactly what I wanted. I always thought it was cool, but it never really caught on. Android killed off support a few years ago. You can still use it with Windows, but I mostly use a Chromecast now for convenience.

Jellyfin is the way