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/common.ts

@@ -0,0 +1,25 @@
+import { z } from "zod/v4-mini";
+
+export const idSchema = z.number();
+export type Id = z.infer<typeof idSchema>;
+
+export const entityLivingSchema = z.object({
+	id: idSchema,
+	updatedAt: z.string(),
+	deleted: z.optional(z.literal(false)),
+});
+export type EnityLiving = z.infer<typeof entityLivingSchema>;
+
+export const entityToombstoneSchema = z.object({
+	id: idSchema,
+	updatedAt: z.string(),
+	deleted: z.literal(true),
+});
+export type EntityToombstone = z.infer<typeof entityToombstoneSchema>;
+
+export const entitySchema = z.discriminatedUnion("deleted", [entityLivingSchema, entityToombstoneSchema]);
+export type Entity = z.infer<typeof entitySchema>;
+
+export function defineEntity<T extends {}>(fields: T) {
+	return z.discriminatedUnion("deleted", [z.extend(entityLivingSchema, fields), entityToombstoneSchema]);
+}