Which flags beyond strict do you turn on, such as noUncheckedIndexedAccess?

None of these are part of strict, and none are on by default (a strict-only config accepted every violation in the example below on 5.9.3 and 7.0.2). I add them deliberately.

• noUncheckedIndexedAccess (4.1). Reading through an index signature or an array index adds | undefined: nums[0] is number | undefined. It is the most valuable one, because out-of-range reads are a real runtime source of undefined that strictNullChecks cannot see. Cost: you narrow or use ?? at each read. Tuple positions and for...of elements are unaffected; .at() already returns T | undefined.
• exactOptionalPropertyTypes (4.4). theme?: "dark" | "light" then means "absent or one of these", not "or undefined". Writing { theme: undefined } is an error. Turn it on when presence matters at runtime (in, Object.keys, spread). The 4.4 notes warn of friction with existing typings; it requires strictNullChecks.
• noImplicitOverride (4.3). A method that overrides a base member must say override, so renaming a base method breaks subclasses visibly instead of silently orphaning them. override on a member the base lacks is an error with or without the flag.
• noImplicitReturns. Every code path must return a value when any path does.
• noFallthroughCasesInSwitch. A non-empty case must break, return or throw.
• noPropertyAccessFromIndexSignature (4.2). Index-signature keys need obj["key"], which signals "might be absent". It is a style flag.

I leave noUnusedLocals and noUnusedParameters to the linter, which can auto-fix and can be set per rule.

// TypeScript 7.0.2, 6.0.3 and 5.9.3; strict plus the four flags below
const nums = [10, 20, 30];
const first: number = nums[0];
// Error TS2322: Type 'number | undefined' is not assignable to type 'number'.
const second = nums[1] ?? 0; // OK: number

interface Opts { theme?: "dark" | "light" }
const opts: Opts = { theme: undefined };
// Error TS2375: Type '{ theme: undefined; }' is not assignable to type 'Opts' with 'exactOptionalPropertyTypes: true'. Consider adding 'undefined' to the types of the target's properties.
const empty: Opts = {};
console.log(Object.keys({ theme: undefined }), Object.keys(empty));
// → [ 'theme' ] []

class Base { setup() {} }
class Child extends Base { setup() {} }
// Error TS4114: This member must have an 'override' modifier because it overrides a member in the base class 'Base'.

function label(c: boolean): string | undefined {
  if (c) { return "yes"; }
}
// Error TS7030: Not all code paths return a value.

• Expecting nums[i] inside for (let i = 0; i < nums.length; i++) to be safe. It stays number | undefined (checked), as the 4.1 notes say. Use for...of, or read once into a const and narrow.
• Assuming narrowing works on any key. With const i = 1, if (nums[i] !== undefined) narrowed nums[i]; with let j it did not (7.0.2).
• Enabling exactOptionalPropertyTypes and then writing Partial<Opts> with undefined. Partial<Opts> stayed exact and rejected { theme: undefined } (TS2375). Say theme?: "dark" | undefined where undefined is intended.
• Expecting noImplicitReturns to exempt a return type that includes undefined. The label function above still errors (TS7030); add return undefined.