While I typically recommend my Keys module for dealing with this kind of input, this would be one of the few scenarios in which I would seriously consider using ContextActionService.
You have a valid question, that is, "What is the best way to manage contextual actions?"
The best solution is usually going to come in the form of seeing whether Roblox has any built-in C or C++ functions you can leverage to accomplish your task, as Roblox doesn't use LuaJIT so "native" functions are typically going to be faster than Lua solutions if your scripts spend tremendous amounts of resources in a specific function, such as a recursive raycast distance checker.
Here is my very not humble opinion.
Stop with Rays. Are you shooting at interactive objects or trying to find distance? If you are shooting, you might even be able to use Mouse.Hit, which is the automatic raycast Roblox performs anyway.
If you aren't, then maybe magnitude would be much more efficient, but then you run into the issue of interacting through walls.
Well maybe there is an even more efficient way. A way of detecting proximity to end all ways of detecting proximity. And it is.... Invisible parts.
Think about it. It comes with two events: Touched and TouchEnded. Perfect for creating a boundaries system with perfect detection of when a player enters and leaves the area in which they should be prompted with an interaction button or a GUI signaling, "Now Leaving Kawaii Waifu Pillow Store". Perfect detection systems are indeed possible!
What? Am I hearing you aren't a big believer in the integrity of Roblox Part event-firing? Thou heretic! Well, I guess that's why we have GetTouchingParts.
I personally recommend a conservative balance between using both the events and the function aforementioned. You'd probably want to trust the detection of large zones to events, and possibly use the function when you aren't entirely convinced the events will be reliable.
I actually haven't written anything like this, and the last time I looked at a module for this was a while ago. I'd probably experiment initially with trusting the events, and then where it doesn't work I would make trade-offs.
A trade-off you might-make, for example, is you might try detecting whether they are in the room with a ton of interaction objects using a large transparent part that fills the room, and use the function to check which one should prompt them.
Good luck! I typed this up on my phone in the late hours of the school-night, but I hope something I said inspired you to create a better system.
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Thanks for the answer! This resembles my currently implementation of this mechanic, though I am looking forward to see if other users find a more effective way that will not cause as much client lag when there's a large amount of objects.