A Lord of the Rings-sized campaign history. Dimmers on the lights. Fingertip access to several seasons of Game of Thrones soundtracks.
There are all sorts of ways to get players into their characters' heads, but what rules does your game use to support immersion? Should immersion be part of the rules?
For example, when I ask for rolls to determine turn order, I ask PCs to use the attribute that best reflects the character's readiness for conflict. This changes the thought process from "roll a die and add what the rules require" to "what was my character thinking or doing when this conflict started?"
You highlight a great example. My Traveller games are often very much like that. I will let the Travellers choose how they react to combat/exploration/social dynamics based on what the Traveller is equipped with. Your Traveller has no combat skills, so what do they do in a fight? Well, maybe they have good computer skills and hack a local terminal to turn the environment against their foes. Maybe they apply their tactics knowledge and lead the team. Its up to the Travellers to help narrate and decide how their character deals with a myriad of situations.
Now the above is pretty difficult to do in systems that have a detailed, intricate, and nuanced combat rule set. Sometimes it can feel like waving away the rules, or disappointing to folks who spend a lot of time figuring out how to interact with them. So, I think there is a fine line to walk that will vary from combat systems in general.
Back when I played in a
Kingmaker PF1 campaigns, the GM wanted the kingdom management to be more immersive and less mechanical. All they did was hide the numbers from us players, yet held to the mechanical ruleset. The result was pretty bad in that we had no idea the impact of our choices. A town needs a mill right? Will that help with economics, security, loyalty, etc..? We had no idea but sure enough the mechanics were being adjusted behind the screen. We had to have a number of discussions on this and many lessons were learned.
Fast forward to today and I am in a
War for the Crown campaign also for PF1. Currently, we are helping build back up a down trodden backwater village. Our goal is to build a presence in the area and effect politics. Unlike Kingmaker, this time we have a series of places that exist, but have stories to explore. The swamp pump house was used to keep the water ways from flooding. Investigating why they have stopped working is an adventure. Clearing up the issue allows ferries to resume service speeding up overland travel. Sometimes there are enemies in the way to fight, sometimes there is some obstacle to overcome. Each place has a beneficial result for engaging. We understand the stakes, and thus, are informed about our decisions. More importantly, it has us engaging the campaign and not just winging it on player whims.
The point of the stories is that immersive rules are tricky. I think you need the right balance of mechanics and player agency. There is a difference between the rules indicating exactly how the game is played, and how one might play the game with a provided toolset. The former or latter are largely dependent on game system design. A bespoke system should lean heavily into the themes the game is supposed to support. A general RPG system, should remain vague and provide many options to both GM and player on how to engage play. YMMV.