Refactor API types and sync logic

Rename and refactor the types passed over the API to be based on an
entity that's either living or a tombstone.  A living entity has a
deleted property that's either undefined or false, while a tombstone
has a deleted property set to true.  All entities have a numeric id
and an updatedAt timestamp.

To sync entities, an array of replacements are passed around. Living
entities are replaced with tombstones when they're deleted. And
tombstones are replaced with living entities when restored.

shared/types/api.ts

@@ -0,0 +1,111 @@
+import { z } from "zod/v4-mini";
+import { defineEntity, idSchema, type Id } from "~/shared/types/common";
+
+export interface ApiAccount {
+	id: Id,
+	type: "anonymous" | "regular" | "crew" | "admin",
+	/** Name of the account. Not present on anonymous accounts */
+	name?: string,
+	interestedEventIds?: number[],
+	interestedEventSlotIds?: number[],
+	timezone?: string,
+}
+
+export const apiAccountPatchSchema = z.object({
+	name: z.optional(z.string()),
+	interestedEventIds: z.optional(z.array(z.number())),
+	interestedEventSlotIds: z.optional(z.array(z.number())),
+	timezone: z.optional(z.string()),
+});
+export type ApiAccountPatch = z.infer<typeof apiAccountPatchSchema>;
+
+export const apiSubscriptionSchema = z.object({
+	type: z.literal("push"),
+	sessionId: z.number(),
+	push: z.object({
+		endpoint: z.optional(z.string()),
+		expirationTime: z.nullish(z.number()),
+		keys: z.record(z.string(), z.string()),
+	}),
+});
+export type ApiSubscription = z.infer<typeof apiSubscriptionSchema>;
+
+export interface ApiSession {
+	id: Id,
+	account?: ApiAccount,
+	push: boolean,
+}
+
+export const apiScheduleLocationSchema = defineEntity({
+	name: z.string(),
+	description: z.optional(z.string()),
+});
+export type ApiScheduleLocation = z.infer<typeof apiScheduleLocationSchema>;
+
+export const apiScheduleEventSlotSchema = z.object({
+	id: idSchema,
+	start: z.string(),
+	end: z.string(),
+	locationIds: z.array(idSchema),
+	assigned: z.optional(z.array(z.number())),
+	interested: z.optional(z.number()),
+});
+export type ApiScheduleEventSlot = z.infer<typeof apiScheduleEventSlotSchema>;
+
+export const apiScheduleEventSchema = defineEntity({
+	name: z.string(),
+	crew: z.optional(z.boolean()),
+	host: z.optional(z.string()),
+	cancelled: z.optional(z.boolean()),
+	description: z.optional(z.string()),
+	interested: z.optional(z.number()),
+	slots: z.array(apiScheduleEventSlotSchema),
+});
+export type ApiScheduleEvent = z.infer<typeof apiScheduleEventSchema>;
+
+export const apiScheduleRoleSchema = defineEntity({
+	name: z.string(),
+	description: z.optional(z.string()),
+});
+export type ApiScheduleRole = z.infer<typeof apiScheduleRoleSchema>;
+
+export const apiScheduleShiftSlotSchema = z.object({
+	id: idSchema,
+	start: z.string(),
+	end: z.string(),
+	assigned: z.optional(z.array(z.number())),
+});
+export type ApiScheduleShiftSlot = z.infer<typeof apiScheduleShiftSlotSchema>;
+
+export const apiScheduleShiftSchema = defineEntity({
+	roleId: idSchema,
+	name: z.string(),
+	description: z.optional(z.string()),
+	slots: z.array(apiScheduleShiftSlotSchema),
+});
+export type ApiScheduleShift = z.infer<typeof apiScheduleShiftSchema>;
+
+export const apiScheduleSchema = defineEntity({
+	id: z.literal(111),
+	locations: z.optional(z.array(apiScheduleLocationSchema)),
+	events: z.optional(z.array(apiScheduleEventSchema)),
+	roles: z.optional(z.array(apiScheduleRoleSchema)),
+	shifts: z.optional(z.array(apiScheduleShiftSchema)),
+});
+export type ApiSchedule = z.infer<typeof apiScheduleSchema>;
+
+export interface ApiAccountUpdate {
+	type: "account-update",
+	data: ApiAccount,
+}
+
+export interface ApiScheduleUpdate {
+	type: "schedule-update",
+	updatedFrom?: string,
+	data: ApiSchedule,
+}
+
+export type ApiEvent =
+	| ApiAccountUpdate
+	| ApiScheduleUpdate
+;