in reality, when your being handed off from approach to approach controller they will know weather your on Flight following, IFR, ETC.
In your case because sometimes IF doesnt always have a center freq and noone ever knows what to do because people dont fly above 18000 that often. Requesting flight following should only come from the pilot then the controller who will be vectoring you INTO KSAN will ask for your intentions or in the real world… and If you had a squawk code
checks in with San Diego Approach
N1TJ- " approach, N1TJ with you, level 3000"
SD App. - “N1TJ, radar contact, 10 miles north of San Diego, say approach request"
N1TJ- " location checks, requesting ( vectors, ILS or, GPS, or visual approach) to runway XX"
SD App. " N1TJ, roger expect ( vectors, ILS or, GPS,) to runway XX, turn HDG XXX” OR " N1TJ, San Diego is @ your 11 olcock 10 miles contact when you have it in sight"
KEYWORD: EXPECT! so from here on out approach will now vector you in for whatever. and get you on the approach course before handing you down to tower.
your expecting a visual approach. SD App will let you know you are cleared for the visual approach. in which case everything is up to you… and he will simply hand you off to the Tower when you are in their airspace and you will let Tower know you are on the visual for XX rwy.
Hope this elaborates on some of the topic. and is helpful when it comes to understand how ATC will be guiding you.