VSCodium
Building on the other responses to this question above, to be able to use some of the latest features VSCodium might be your best option, unless you need Microsoft Account-enabled features. As of April 19, 2023 I was able to run the latest release of VSCodium 1.77.3.23102 32-bit build from the ZIP archive on 64-bit Windows 7 SP1. Note, I did not test on 32-bit Windows 7 but I imagine the 32-bit builds should run as well. Note there are messages indicating that VSCodium will soon stop receiving updates for Windows 7 / Windows Server 2008 R2. The funny thing is that upon clicking on the Learn More hyperlink or button you are directed to a URL from the VS Code documentation indicating versions greater than 1.70 will not run on Windows 7.
Visual Studio Code
If you are looking specifically for VS Code, I was able to find the other 32-bit (and 64-bit) build links from the VS Code Documentation FAQ page under heading "Previous Release Versions" which I found from a StackOverflow question (# 49346733) titled "How to downgrade vscode": (Not linking to these relatively easy to find FAQ and SO question pages as I don't have enough reputation to post more than 8 links at this time and would prefer to provide direct links to the builds for download)
32-bit builds:
ZIP: https://update.code.visualstudio.com/1.70.2/win32-archive/stable
System Installer: https://update.code.visualstudio.com/1.70.2/win32/stable
User Installer: https://update.code.visualstudio.com/1.70.2/win32-user/stable
64-bit builds:
ZIP: https://update.code.visualstudio.com/1.70.2/win32-x64-archive/stable
System Installer: https://update.code.visualstudio.com/1.70.2/win32-x64/stable
User Installer: https://update.code.visualstudio.com/1.70.2/win32-x64-user/stable
With regard to the final VS Code update for Windows 7, version 1.70.3 for the ZIP archive builds, I was able to find direct links to the latest version 1.70.3 by clicking on the Gear icon in the lower left and using the built-in Download Updates option which directed me to the following URLs for the 32-bit and 64-bit editions:
32-bit VS Code 1.70.3 ZIP archive:
https://az764295.vo.msecnd.net/stable/a21a160d630530476218b85db95b0fd2a8cd1230/VSCode-win32-ia32-1.70.3.zip
64-bit VS Code 1.70.3 ZIP archive:
https://az764295.vo.msecnd.net/stable/a21a160d630530476218b85db95b0fd2a8cd1230/VSCode-win32-x64-1.70.3.zip
Unfortunately, I could not find a direct URL to download the system or user installers for version 1.70.3, although the built-in updater (accessed from the Gear icon menu in the lower left) seemed to download an updater package, creating a new directory vscode-update-[system/user]-[ia32/x64] underneath C:\Users<UserName>\AppData\Local\Temp\ under which an .EXE file and sometimes a .flag file were written. For the system installer versions I received a UAC prompt and was able to track down the directory and file locations from there. (Though there was no UAC prompt for the user installer versions, I did find similar directories adjacent to the system directories under AppData\Local\Temp which I am assuming are the updaters for those versions). Here are the SHA-256 hashes of those files, their file sizes and locations:
32-bit system installer updater to 1.70.3:
Sub-directory of AppData\Local\Temp: vscode-update-system-ia32\
File name: CodeSetup-stable-a21a160d630530476218b85db95b0fd2a8cd1230.exe
SHA-256 Hash:
0c64ea2647a54b7cdc4d3a3c91fbcebbe43b250417c75c0437fca252572a692d
Size: 79,271,448 bytes
64-bit system installer updater to 1.70.3:
Sub-directory of AppData\Local\Temp: vscode-update-system-x64\
File 1 name: CodeSetup-stable-a21a160d630530476218b85db95b0fd2a8cd1230.exe
SHA-256 Hash of file 1: 63a0e5beb949cbf70a8e8e78a8f2d0d8be48e6f59966769789f236fb7643711c
Size of file 1: 82,838,336 bytes
File 2 name: CodeSetup-stable-a21a160d630530476218b85db95b0fd2a8cd1230.flag
SHA-256 Hash of file 2: 807d0fbcae7c4b20518d4d85664f6820aafdf936104122c5073e7744c46c4b87
Size of file 2: 4 bytes
32-bit user installer updater to 1.70.3:
Sub-directory of AppData\Local\Temp: vscode-update-user-ia32\
File name: CodeSetup-stable-a21a160d630530476218b85db95b0fd2a8cd1230.exe
SHA-256 Hash: 1d136adc8d36a7785bd2379b643c003caeace78a3c122910ec83ec76c76cfce5
Size: 79,271,592 bytes
64-bit user installer updater to 1.70.3:
Sub-directory of AppData\Local\Temp: vscode-update-user-x64\
File name: CodeSetup-stable-a21a160d630530476218b85db95b0fd2a8cd1230.exe
SHA-256 Hash: b1332b48970ade9aaf4f0948fee417cabd0207aca44985798f4f941afefa32f3
Size: 82,838,544 bytes