perf(react-router): remove root search schema type and unused type parameters from route options

[chorobin]

• remove root search schema as it doesn't seem to be needed
• remove unused type parameters for route options
• added tests to cover index routes and root search schema

[nx-cloud]

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✅ Successfully ran 4 targets

• nx run-many --target=test:e2e:replay
• nx affected --targets=test:format,test:eslint,test:unit,test:build,build --parallel=3
• nx affected --target=build --exclude=examples/**
• nx affected --target=test:types --exclude=examples/**

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[chorobin]

Reduces instantiations a bit because we don't need to exclude/omit RootSearchSchema
Before

> tsc --extendedDiagnostics

Files:                         644
Lines of Library:            38411
Lines of Definitions:        82809
Lines of TypeScript:         19639
Lines of JavaScript:             0
Lines of JSON:                   0
Lines of Other:                  0
Identifiers:                134746
Symbols:                    326768
Types:                      115290
Instantiations:             826289
Memory used:               392053K
Assignability cache size:    47858
Identity cache size:          8641
Subtype cache size:           2426
Strict subtype cache size:     413
I/O Read time:               0.10s
Parse time:                  0.78s
ResolveModule time:          0.16s
ResolveTypeReference time:   0.01s
ResolveLibrary time:         0.02s
Program time:                1.19s
Bind time:                   0.32s
Check time:                  5.96s
printTime time:              0.00s
Emit time:                   0.00s
Total time:                  7.47s

After

> tsc --extendedDiagnostics

Files:                         644
Lines of Library:            38411
Lines of Definitions:        82800
Lines of TypeScript:         19639
Lines of JavaScript:             0
Lines of JSON:                   0
Lines of Other:                  0
Identifiers:                134667
Symbols:                    326556
Types:                      115064
Instantiations:             816475
Memory used:               386904K
Assignability cache size:    47482
Identity cache size:          8539
Subtype cache size:           2426
Strict subtype cache size:     413
I/O Read time:               0.08s
Parse time:                  0.59s
ResolveModule time:          0.13s
ResolveTypeReference time:   0.00s
ResolveLibrary time:         0.02s
Program time:                0.92s
Bind time:                   0.27s
Check time:                  5.47s
printTime time:              0.00s
Emit time:                   0.00s
Total time:                  6.65s

[chorobin]

Don't merge just yet. Just want to double check everything

[SeanCassiere]

Just want to confirm the RootSearchSchema type wasn't being used for Router inference right? So it's getting nuked.

[chorobin]

Just want to confirm the RootSearchSchema type wasn't being used for Router inference right? So it's getting nuked.

From what I understand from conversations with @schiller-manuel the users don't use this type unlike SearchSchemaInput? It seems like there was a bug some time ago confusing the root route and the index route. But this doesn't seem to be a problem anymore. There's been a lot of changes to the types since then so if we don't need it, I'd remove it because it just means we need to check for it all the time