Have you fully configured interface 3’s IPv4 settings? Specifically, have you configured a default gateway for it? If you haven’t, Plex Media Server will not see it as an available network interface.
Windows will display a warning when you save a configuration where there are multiple default gateways defined. It’s intended to prevent situations where a system has multiple paths to off-network destinations (e.g. the Internet).
You’ll also need to configure the interface metric value for each interface where you define a default gateway (advanced button on the IPv4 properties). This is to ensure Windows has a clearly defined priority for which gateway to use. The lower the number, the higher the priority. If you’d like interface 1 to be used for outbound traffic to the Internet, set it to a lower number, such as 10. Then, give interface 3 an interface metric of 20. Perhaps interface 2 should in their somewhere as well.
Some of the above may change depending on what you’re trying to accomplish by using multiple network interfaces on your server. Is it to segregate traffic or provide a higher-speed link for data storage? Or something else?