Update: Make sure you replace the config.vdf file with the one in this Google Drive link brought to you by a wonderful user by the name ch738:
https://drive.google.com/file/d/1nIkO33f2tCAc6Oueen_HHIJIs4YXldLq/edit

Also make sure you have 7-Zip or Winrar to extract the Steam client. Everyone else tells you to do this with .zip and .rar files, but I thought to do this for anyone who still hasn't figured it out yet or needs me to say this from force of habit or whatever. Also, make sure you have the region set to Germany - Dsseldorf. The download speed may be a lot slower depending on your location, but it should be able to download games and software and update them at the very least.

This is a mostly unmodified 7-zip package containing the last known build of Steam to work on Windows XP and Windows Vista (without the extended kernel). The only real modification is that automatic updates have been disabled (just like the November build).
A more definitive version of this build can be downloaded in this video's description.

I've included the package info converter zip file to convert a packageinfo.vdf file from a modern machine to convert to the old format, this is also useful in getting the old theme on Windows 7 and beyond. I've also included an executable of the roots certificate update for Windows XP and a zip file containing the same update for Vista.

Lastly, keep in mind that as of late, an update to the Steam servers has broken the ability to install games onto the old client by normal means. You'll have to move the entire steamapps folder to your XP (or Vista) machine to play games, and even then, Steamworks Common Redistributables has to be updated to even play the games in the first place. I suggest just playing the games without the Steam client if possible or finding a copy of the redistributables and playing offline if possible, and perhaps using cracked (not recommended) or GOG versions of the games and placing them into their respective folders. Simply put, Steam on XP and Vista is most definitely coming to a close soon (unless there's an update that unintentionally reverses this issue).

How to install:

1. Install the latest version of Steam.

2. Delete the files from the Steam directory, except for uninstall (if you want to later uninstall Steam). The directory is usually C:\Program Files\Steam, or C:\Program Files (x86)\Steam if you have a 64-bit installation of XP or Vista (without the extended kernel).

3. Extract the files from the included .7z into the Steam directory.

4. Take a packageinfo.vdf from the appcache of a modern machine with Steam, and run it under the included package info converter. This will convert it to the old format suitable for the old UI. This is also useful for restoring the old UI on a modern computer.

5. Update root certificates. The .zip file labeled rootsupd.zip has the updates for Vista, the standalone .exe contains the updates for XP.

6. Paste the config.vdf file included in the Google Drive link above into the Steam directory. This should provide the latest content servers to install your games from. Otherwise you'll have to copy and paste the games and .acs files to your XP machine everytime you want to install a new game.

7. Open up Steam and sign in as you always do, you know the drill. Also stated above, if you want the full 2018 Steam experience, use this client instead (it contains the package info converter in the appcache folder):
https://mega.nz/file/GtxEnRgS#4wofSpWfYy0r14_7vc8pnpvWSxI7kX2gFOUmaZj0Ugc
https://drive.google.com/file/d/1ofwuPfvpRtLl3q5KTXlCBDW7m1TKoGYm/view