I posted on here a while ago about moving from a desktop to a laptop (still having trouble finding a laptop). Because 4 TB SSDs are too expensive I'll likely be using a 2 TB SSD and splitting it between Windows & Linux. To save space I'm thinking I'd like to install a game and or my Steam Library on an external SSD, would this work if both the SSD's and the computer's usb ports were usb 3? Thanks.

I'd also be splitting this external SSD, probably half ext4 and half NTFS.

You may need to alter the config file to look for/use the libraries, (unless they have been programmed in), it should work.

I know with Steam you can select visible drives/directories where you want to install your Steam game library. So at least with Steam it should be configured automatically? At least that's my thinking.

Yes this will work 'as intended' with Steam - just create a new library on the external drive once its mounted. If the mount point changes (e.g. because you mount by block ID vs UUID) you may have to re-add it once it re-mounts. It should work fine with other games (not on Steam) as well, if you mount it somewhere you have read/write access to (or chown it). No requirement for USB 3 even - just a 'nice to have' for performance.

Note that you may not (as in, probably will not) be able to install the game 'once' - e.g. say you wanted to install Half-Life 2 in Windows, and also use it in Linux, it will generally need both the Windows and Linux version(s) of the game installed. This is kind of a weird corner-case (I can't imagine why you'd want two ports of the same installed), but the bigger takeway is expect to have two Steam libraries on separate partitions (also there's few file systems that are truly 'common' between Windows and Linux, as you point out).

All of this should also work with no problem for non-Steam games as well, for example those downloaded from GOG - the computer won't regard the external drive as 'special' in any way, its just another block device onto which it can write data. Just point the installer at whatever directory you create, and away you go (and this will apply in both Windows and Linux). The only thing to keep in mind - don't accidentally eject the USB drive (it won't hurt anything, you'll just lose the drive until you reconnect it) - in Windows this is probably easier to do by accident with the 'Safely Remove Hardware' prompt rolling all devices up into a menu, whereas most Linux DEs will show an eject icon per-device in their respective file managers.

https://support.steampowered.com/kb_...7418-YUBN-8129 (the GUI examples will apply in linux as well, but the device names will be different)
https://www.cyberciti.biz/faq/linux-...-update-fstab/ (this was the easiest guide I could find to setup fstab with UUID - its really quite simple, and will be more resilient than using the block ID (e.g. /dev/sda) especially when dealing with removable media)

Finally: you may not need an SSD for this role. Very few benchmarks show significant benefits for SSDs to gaming (I know this cuts counter to the 'conventional wisdom' of many online echo chambers), because most games are computationally bound, rather than disk bound (and modern mechanical hard drives have also gotten seriously fast to boot). Just food for thought if you're weighing cost/capacity - I'm not at all opposed to an SSD for an internal drive in a laptop (for a variety of reasons it's a good idea), but for an external game drive I'd probably be inclined to save my money and get a large-ish 3.5" external instead (then again, I also don't see how a single 2TB SSD is either 'cheap' or 'too small' even for a dual-booting system, so perhaps our use cases are quite dissimilar).

For the "corner case" of having steam installed on both windows and linux in a dual boot scenario you would need 2 separate partitions on the external drive. One would be formatted at either fat32 or ntfs for use with windows, the other would be formatted as ext4 or ? for use with linux. Then the extra space would be available for each and they would not conflict. It would require also that you install the game twice, once in each OS.

I can't see where the dual use would be needed unless you were installing games that did not work in steam and needed to be installed individually. Games in steam should work regardless of the OS you were running.

Linux can effectively utilize ntfs partition. I have software installed on ntfs. Such partition can be shared between systems. But it may not work for sharing games. Perhaps it can be resolved by digging more in Windows registry.

Yes - you would need separate partitions for Windows/linux, and likely cannot just take a game installed in one and run it in the other - they will have very different executable and API structures (specifically talking about games that are 'universal'). Taking a 'windows install' and putting it into wine, or a wine install and putting it into windows, may be possible with a non-trivial (i.e. non-automated) level of intervention, as igadoter points out.