fix(visits): reach every lab result, condition, document and visit from the link pickers

The visit form's lab picker offered the newest 200 results, the condition
picker the newest 100 conditions, the document pickers the newest thousand
documents and the document sheet's visit picker the newest 100 visits.
On a long record everything older could not be linked.

Each picker now opens on the records around the date of the thing being
linked, pages older and newer from there, and searches through the list
route itself. Records already linked always show, from the labels the
record's own read carries and from what was picked in the sheet.

The lab list takes a q filter over analyte and panel, the condition list
from/to/q/offset/sortDir, and the visit list an offset.

src/lib/validations/encounters.ts

@@ -164,6 +164,11 @@ export const encounterListQuerySchema = z
      */
     episodeId: id.optional(),
     limit: z.coerce.number().int().min(1).max(200).optional(),
+    /**
+     * Rows to skip in each arm, for a picker that pages a long history in
+     * `limit`-sized steps inside a date window.
+     */
+    offset: z.coerce.number().int().min(0).max(100_000).optional(),
   })
   .strict()
   .refine((q) => !(q.from && q.to) || q.from <= q.to, {

src/lib/validations/illness.ts

@@ -136,6 +136,17 @@ export type IllnessEpisodeResolve = z.infer<typeof illnessEpisodeResolveSchema>;
 export const illnessEpisodeListQuerySchema = z.object({
   limit: z.coerce.number().int().min(1).max(100).optional(),
   includeResolved: z.union([z.literal("true"), z.literal("false")]).optional(),
+  /**
+   * Paging and a date window over the onset, for a picker that opens on the
+   * episodes around a visit and pages older or newer from there.
+   */
+  offset: z.coerce.number().int().min(0).max(100_000).optional(),
+  from: z.iso.datetime({ offset: true }).optional(),
+  to: z.iso.datetime({ offset: true }).optional(),
+  /** Onset order; newest first by default. */
+  sortDir: z.enum(["asc", "desc"]).optional(),
+  /** Case-insensitive substring over the episode's label. */
+  q: z.string().trim().min(1).max(120).optional(),
 });
 
 /* ── day-log capture (one row per day of an episode) ─────────────── */

src/lib/validations/labs.ts

@@ -284,6 +284,11 @@ export const listLabResultsSchema = z.object({
   biomarkerId: z.string().trim().min(1).max(64).optional(),
   analyte: z.string().trim().min(1).max(120).optional(),
   panel: z.string().trim().min(1).max(120).optional(),
+  /**
+   * Case-insensitive substring over the analyte and the panel name, so a
+   * picker can find one result in a long history without paging to it.
+   */
+  q: z.string().trim().min(1).max(120).optional(),
   from: z
     .string()
     .datetime()