Vans RV-14 pilot reported a NMAC with an IFR air carrier flight that was being vectored for an ILS approach to a nearby airport.

Narrative

On the final leg of a half hour flight departing ZZZ - ZZZ1 - ZZZ I was descending from about 11000 to about 9000 feet heading directly to ZZZ. ZZZ2 was about 8 miles to my port side in my aircraft; when I heard and saw a heavy aircraft flying about 300-500 feet below me and just behind my aircraft. I was informed that the flight was on an ILS inbound for runway XX to ZZZ3. They were apparently informed by their radio IFR center/control of my plane being a close target; thus the TCAS-RA. I believe it was likely my radio was still on 122.7 because I had landed ZZZ1 and taken off a few minutes earlier within this flight. My home airport & ZZZ2 frequencies are both 122.8 therefore I neither heard of the incoming flight to ZZZ2 airport or from their controller. And it should be noted ZZZ2 is an uncontrolled airport and I was completely outside their general airspace. It was neither class D;C or B airspace. I was flying perpendicular to the other aircraft in G or E airspace.I have ADSB equipment on board with two Advance Flight System EFIS (Electronic Flight Instrument System). I saw the target on the flight display;some moments prior to the mid air near collision; but it was about thirty miles out to the NE and therefore did not seem a factor. This target was among others that were distant. I did not continue my surveillance of this target to make heading or altitude changes prior to this event; and it seems; neither did the other traffic. At least the other traffic did not make changes until the last seconds or not significant ones. That part I can not know. And I do not have the flight records to see both flights. I am thankful both are alive! My assessment of what I could do differently: 1. Follow targets longer without assumptions. ADSB targets at ZZZ4 or ZZZ5 are far too numerous to manage in the way I am suggesting. They become clutter and distractions inside the cockpit instead of outside scanning. But in general greater attention to even distant targets was needed in this case and this and most environments than I did. I did know that ZZZ2 also serves transport jet traffic but in this case did not make that connection about this target soon enough to avoid the danger. 2. I changed my frequency back to 122.8 following the landing and take off at ZZZ1 I would have heard the reporting inbound traffic target coming into ZZZ6.3. This comment relates to #2. I always use flight following for cross country flights. But I never use Flight Following for short scenic flights in my local area. In addition; I know of no pilots who do. However keeping local frequencies tuned to nearby airports could have been valuable in this event to be avoided!4. I can never know what the thinking is happening in the other pilot or target's head. But I wonder why the other aircraft assumed they had the right to continue their direct ILS approach without seeing or changing their flight path to a greater degree too. I was a broadside view out their window. But I guess too small a bug target to see. Likewise; when did they first see my target? But all this in # 4 is irrelevant to my growth as a pilot!!!As another side note; I am engaging with a CFII and other training to enhance my strategies and skills. I will make this another significant lesson in my aviation journey to make the skies more safe for me and others! Thank you for your work in that mission!