I installed both Sinytra Connector, Forgified Fabric API, and even Connector+ installed, but Continuity still doesn't load; it seems to not even recognize connector as being installed.

Mod List for reference:

• .connector
• 3d-Skin-Layers [1.8.1]
• Advanced Netherite [2.3.0]
• Advancement Plaques [1.6.8]
• Almanac [1.0.2]
• AmbientSounds [6.1.12]
• Amplified Nether [1.2.11]
• AppleSkin [3.0.7+mc1.21]
• Architectury [13.0.8]
• AttributeFix [21.1.2]
• AzureLib [3.0.20]
• Balm [21.0.46]
• Better End [21.0.11]
• Better Nether [21.0.11]
• Better Third Person [1.9.0]
• BetterF3 [11.0.3]
• Biomes O' Plenty [21.1.0.12]
• Bookshelf [21.1.67]
• Chat Heads [0.13.18]
• Cherished Worlds [10.1.1+1.21.1]
• ChoiceTheorem's Overhauled Village [${version}]
• Chunky [1.4.23]
• Cloth Config v15 API [15.0.140]
• Clumps [19.0.0.1]
• Collective [8.3]
• Connector Extras [1.12.1+1.21.1]
• Continuity [3.0.0+1.21.neoforge]
• CorgiLib [5.0.0.4]
• Create [6.0.6]
• Create Crafts & Additions [NONE]
• Create Slice & Dice [4.0.1]
• Create: Connected [1.1.6-mc1.21.1]
• Create: Garnished [2.1.6.2]
• CreativeCore [2.13.7]
• Creeper Overhaul [4.0.6]
• Cristel Lib [1.2.8]
• Cubes Without Borders [3.0.0+mc1.21]
• Curios API [9.0.15+1.21.1]
• Curios API [9.5.1+1.21.1]
• Cut Through [21.1.0]
• Deeper and Darker [1.3.4]
• Deimos [2.2]
• Drippy Loading Screen [3.0.12]
• Dungeons and Taverns [1-v4.4.4]
• Dynamic Crosshair [9.7.1]
• Dynamic FPS [3.9.5]
• EC Samurai Dynasty Plugin [1.1.5]
• EXP Counter [2.1]
• End's Delight [2.5.1+neoforge.1.21.1]
• Enderman Overhaul [2.0.2]
• Entity Model Features [2.4.1]
• Entity Texture Features [6.2.9]
• EntityCulling [1.8.1]
• Expanded Combat [3.3.9]
• Expanded Ecosphere [3.4.1.1]
• Expanded Storage [14.2.4]
• FancyMenu [3.6.2]
• Farmer's Cutting: Oh The Biomes We've Gone [1.21.1-2.1-neoforge]
• Farmer's Delight [1.2.8]
• Ferrite Core [7.0.2]
• Forge Config API Port [21.1.3]
• Forgified Fabric API [0.115.6+2.1.1+1.21.1]
• GeckoLib 4 [4.7.6]
• Geophilic [3.4.2]
• GlitchCore [2.1.0.0]
• Golem Overhaul [1.0.1]
• Highlighter [1.1.11]
• Iceberg [1.3.2]
• Immersive Aircraft [1.3.3+1.21.1]
• Incendium [5.4.3]
• Inventory Profiles Next [2.1.9]
• Iris [1.8.12-snapshot+mc1.21.1-local]
• Jade [15.10.2+neoforge]
• Konkrete [1.9.9]
• Kotlin for Forge [4qCjWixP]
• Let Me Despawn [1.5.0]
• Lithium [0.15.0+mc1.21.1]
• Lithostitched [1.4.11]
• Mahou Tsukai [1.21.0-v1.35.18]
• Melody [1.0.10]
• MidnightLib [1.6.9]
• Model Gap Fix [1.21-1.10]
• ModernFix [5.24.1+mc1.21.1]
• Moonlight Lib [1.21-2.19.5]
• Mouse Tweaks [2.26.1]
• Nature's Compass [1.21.1-3.0.2-neoforge]
• NetherPortalFix [21.1.1]
• No Chat Reports [1.21.1-v2.9.1]
• Noisium [2.3.0+mc1.21-1.21.1]
• Nullscape [1.2.12]
• Oh The Biomes We've Gone [2.4.4]
• Oh The Trees You'll Grow [5.0.14]
• Polymorph [1.0.10+1.21.1]
• PrickleMC [21.1.8]
• ProjectE [1.1.0]
• Puzzle [2.0.1]
• Puzzles Lib [21.1.36]
• Reese's Sodium Options [1.8.3+mc1.21.4]
• Remove Terralith Intro Message [1.1]
• Resourceful Lib [3.0.12]
• Resourcefulconfig [3.0.11]
• Ribbits [1.21.1-NeoForge-4.1.2]
• Roughly Enough Items (REI) [16.0.799]
• Samurai Dynasty [0.1.4-1.21.1]
• ShulkerBoxTooltip [5.1.6+1.21.1]
• Sinytra Connector [KrmWHpgS]
• Sodium [0.6.13+mc1.21.1]
• Sound Physics Remastered [1.21.1-1.4.12]
• Stackable [1.3.1]
• Starter Kit [7.4]
• Supplementaries [1.21-3.3.4]
• Tectonic [3.0.1]
• TerraBlender [4.1.0.8]
• Terralith [2.5.8]
• Village Spawn Point [4.6]
• Villager Names [8.2]
• Visual Workbench [21.1.0]
• WaveyCapes [1.6.1.1]
• Waystones [21.1.19]
• William Wythers' Overhauled Overworld [2.3.4]
• Wunderreich [21.0.4]
• Xaero's Minimap [25.2.6]
• Xaero's World Map [1.39.9]
• YUNG's API [1.21.1-NeoForge-5.1.6]
• YUNG's Better Desert Temples [1.21.1-NeoForge-4.1.5]
• YUNG's Better Dungeons [1.21.1-NeoForge-5.1.4]
• YUNG's Better End Island [1.21.1-NeoForge-3.1.2]
• YUNG's Better Jungle Temples [1.21.1-NeoForge-3.1.2]
• YUNG's Better Mineshafts [1.21.1-NeoForge-5.1.1]
• YUNG's Better Nether Fortresses [1.21.1-NeoForge-3.1.5]
• YUNG's Better Ocean Monuments [1.21.1-NeoForge-4.1.2]
• YUNG's Better Strongholds [1.21.1-NeoForge-5.1.3]
• YUNG's Better Witch Huts [1.21.1-NeoForge-4.1.1]
• Yeetus Experimentus [87.0.0]
• create: things and misc [1.0.0]
• e4mc [5.4.1]
• libIPN [6.5.0]
• spark [1.10.124]

Oh, yes. In that case, send a game log file. It contains the list of mods actually loaded.

Your mod list has Connector Extras, but not Connector, so I'm inclined to believe that it actually isn't installed. .connector is a temporary directory and not a mod.

Wouldn't that be "Sinytra Connector [KrmWHpgS]"?

latest.log

Wait that was another error; I had installed fusion temporarily as a fix so I can play (and to bug fix any other errors), I'll check again if it was an issue with the version I had installed.

Update: It doesn't seem to break anymore; it could be an issue with Prism Launcher instead (which I'm using), or something. Sorry for the trouble! It could also have been another mod conflicting with Continuity (I deleted some mods in the process of bug fixing, so it could have been that).

I also have this error (using prism as well)

I'm adding this because I tried making a 1.20.1 modpack with Continuity, and it's given me a similar error (again)

This time the game did show that Connector is there, but just in case, here's more proof:

Thankfully, this time I added Crash Assistant; so here's the latest.log. And some other things that may be helpful:

Prism Launcher log.

Crash log (albeit, I'm not sure how much the crash log will be useful; I don't deal with minecraft crashes that often in a technical sense).

Mod List

I have the same problem with BetterEnd and BetterNether installed... Without these mods everything works fine.