Patch 13.06 Rewired the Client. Here Is the Settings Checklist It Asks for
The 13.06 update merged Home and Lobby into one hub, added Rank Legacy, and left a trail of post-patch crash and frame-drop reports behind it. Before re-auditing anything, look at what 216 pro video-setting profiles in our database actually run: 99% exclusive fullscreen, zero listed VSync on, and a coin flip on Keep Player Centered.

Four bullets, one implication: the client around your settings changed even though your settings did not. Here is the re-audit that is actually worth your time, anchored on what the pros in our database run rather than on superstition.

What moved, in plain terms
Riot folded the pre-game flow into one hub, moved career statistics under a new Competitive tab, and replaced the old per-agent Kingdom gear progression with the Agent Mastery system (patch notes). Gameplay values, crosshair codes, and sensitivity numbers all carried over untouched - nothing in 13.06 silently rewrote your aim. What did change is where things live, which is why the post-patch support boards are busy: people are reporting the client launching into new menus, and a smaller wave reports stutters or lost frames after the update installed (13.06 wiki).
If your game took a performance hit on September 23, work the standard order before blaming the patch: verify game files through the launcher, do a clean GPU driver update, then re-check the official Known Issues list before touching anything inside the game. If all three are clean, the settings pass below tells you which of your toggles the pros would question.
The settings pass, sized by 216 pro profiles
Our player database currently records video settings for 216 pros, and the distribution is about as lopsided as it gets in this game:
Everything else - resolution, refresh rate, the whole competitive display stack - lives in the same settings menus, just two clicks from a different landing page. If you ported your aim from another shooter, the sensitivity converter still does the math for you.

The one toggle the pros cannot agree on
Here is the funnier half of the database: of 213 players with minimap settings recorded, Keep Player Centered is On for 97 and Off for 94 - a literal coin flip among professionals (players hub). Everything else about the minimap has a majority: 44.4% of the 189 players with a known size run the maximum 1.2, 92.1% of 190 keep vision cones on, and 80.6% of 191 play a rotating minimap rather than fixed. The new client does not ask you to resolve the 97-94 disagreement - nobody can. Treat subjective toggles as settled once, then stop re-litigating them every patch.
The other thing 13.06 gave you has no pro-data anchor at all: Rank Legacy, the lifetime ranked-history view in the Competitive Hub (official notes). It is a nice archive, and it pairs well with the rank calculator if you are chasing a specific ladder goal before Act 5 closes on October 14. The client rewired itself; your habits mostly do not need to follow it. Spend ten minutes on the five checklist items above, ignore the rest of the noise, and if something still stutters after all of it, you are holding a driver or Known-Issues problem, not a settings problem - which is exactly what Riot's tracker on the patches hub is for.