chore: enable skipLibCheck to resolve TypeScript compilation issues

[yusukebe]

• Set skipLibCheck to true in tsconfig.json to resolve type checking issues
• Updated jsdom for better compatibility

The author should do the following, if applicable

• Add tests
• Run tests
• bun run format:fix && bun run lint:fix to format the code
• Add TSDoc/JSDoc to document the code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 91.41%. Comparing base (3a5248f) to head (0d40a6f).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #4342   +/-   ##
=======================================
  Coverage   91.41%   91.41%           
=======================================
  Files         172      172           
  Lines       10900    10900           
  Branches     3165     3138   -27     
=======================================
  Hits         9964     9964           
  Misses        935      935           
  Partials        1        1           

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[github-actions]

Bundle size check

	main (3a5248f)	#4342 (90a97d5)	+/-
Bundle Size (B)	18,320B	18,320B	0B
Bundle Size (KB)	17.89K	17.89K	0K

Compiler Diagnostics (tsc)

	main (3a5248f)	#4342 (90a97d5)	+/-
Files	263	270	7
Lines	116,507	121,170	4,663
Identifiers	114,440	118,528	4,088
Symbols	260,109	262,929	2,820
Types	162,704	162,715	11
Instantiations	3,037,417	3,037,429	12
Memory used	272,410K	279,833K	7,423K
I/O read	0.02s	0.02s	0s
I/O write	0s	0s	0s
Parse time	0.66s	0.68s	0.02s
Bind time	0.3s	0.29s	-0.01s
Check time	3.79s	3.73s	-0.06s
Emit time	0s	0s	0s
Total time	4.75s	4.7s	-0.05s

Compiler Diagnostics (typescript-go)

	main (3a5248f)	#4342 (90a97d5)	+/-
Files	233	240	7
Lines	106,406	111,069	4,663
Identifiers	106,180	110,268	4,088
Symbols	353,040	355,968	2,928
Types	287,985	288,018	33
Instantiations	3,544,910	3,544,940	30
Memory used	222,330K	225,103K	2,773K
Memory allocs	9,971,357	10,009,437	38,080
Parse time	0.075s	0.094s	0.019s
Bind time	0.024s	0.019s	-0.005s
Check time	1.6s	1.701s	0.101s
Emit time	0s	0s	0s
Total time	1.707s	1.817s	0.11s

---

Reported by octocov

[github-actions]

HTTP Performance Benchmark

Framework	Runtime	Average	Ping	Query	Body
hono (origin/main)	bun	38,648.65	53,410.87	33,825.14	28,709.95
hono (current)	bun	38,754.96	53,186.33	34,278.14	28,800.41
Change		+0.28%	-0.42%	+1.34%	+0.32%