Technically, there are two ways to resolve these in-game missing texture errors.

now Why do these Texture errors occur while playing?
It's because when you play gmod, there may be some textures and models that you haven't mounted or manually installed. When you play a game without those installed textures, the game will display an Error texture indicating that you are missing the required textures or models for these files.

This is the first method of repair

METHOD NUMBER 1

You should buy and install Half-Life Episodes 1 and 2, and then whenever you open Gmod, there should be a Games option in the bottom right or left corner Check that the installed games called Half Life Episode 1 and 2 have check marks on them. If not, check mark them. If it is mounted, it should have a blue or green checkmark.

If the first method does not work for you, the second method is my preferred option if none of the above did.

METHOD 2 OF SOLUTION

You must manually install those two content sources into your Garry's Mod Addons folder, which is a less time-consuming and simple process.

You must download and install these content sources from this website. You will need either winrar or seven zip to do so.

{LINK REMOVED}https://gmodcontent.com/

Half Life 2: Episode 1 Gameplay
Gameplay in Half Life 2: Episode 2

Once you've located these content sources, select your preferred download servers and then fully download them.

You must first go to Steam and then to your library After that, right-click your Garry's Mod and hover over Manage to see the "browse local files" option. continue with that

After you've done that, you'll be taken to the steam local files where you'll see the files and folders. There will be another folder called "Garry'smod" that you'll press on and then go to the addons folder.

Following that, I will demonstrate how to extract the two zipped files you downloaded from the Gmod content sources.
Place the half-life episode 1 and 2 winrar zipped folders in the addons folder, then right click and select "Extract here." Once both Folders have been fully extracted, Make sure to get rid of any leftover Winrar.Zip folders in your addons to ensure no problems arise.

Exit the folder, restart Gmod, and enjoy your error-free gmod map.