Make birthdays calendar color configurable and expose it via CalDAV

- Add a per-user birthday_calendars table (color, cascade-deletes with
  the user) and GetBirthdayCalendarColor/SetBirthdayCalendarColor in
  internal/db, plus a reservedCalendarNames guard ("birthdays") in
  CreateCalendarWithColor so no real calendar can collide with the
  synthetic one, whether created via the web UI, nidusctl, or CalDAV
  MKCALENDAR.
- Add a "Birthdays" virtual resource card to the dashboard (color
  picker only, no delete/share controls) backed by a new
  ResourceCard.Virtual flag and POST /web/resources/birthdays/color
  handler.
- Extract the birthday-parsing/generation logic shared by the web
  calendar view and CalDAV into internal/birthdays (ParseBirthday,
  Collect, OccurrenceDate, Summary) instead of duplicating it.
- Expose the Birthdays calendar over real CalDAV in
  internal/caldav/backend.go + birthdays.go: it's always listed for
  every user, generates one VEVENT per (contact, year) for a rolling
  window (current year -2..+8) with "🎂 Name (Age)" titles, is
  read-only (Put/Delete/DeleteCalendar all return 403), and its
  Apple/DAVx5 calendar-color is injected from the same per-user
  setting used by the dashboard/web view.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

internal/caldav/birthdays.go

@@ -0,0 +1,156 @@
+package caldav
+
+import (
+	"fmt"
+	"net/http"
+	"path"
+	"regexp"
+	"strconv"
+	"strings"
+	"time"
+
+	ical "github.com/emersion/go-ical"
+	"github.com/emersion/go-webdav"
+	"github.com/emersion/go-webdav/caldav"
+
+	"github.com/yourusername/caldav-server/internal/birthdays"
+)
+
+// birthdaysCalendarName is the fixed, reserved local calendar name the
+// synthetic Birthdays calendar is exposed under (see
+// db.reservedCalendarNames, which prevents a real calendar from ever
+// colliding with it). It has no owner/shared-name segment: it's always
+// computed from the requester's own contacts.
+const birthdaysCalendarName = "birthdays"
+
+// defaultBirthdayColor is the display color for the virtual birthdays
+// calendar when the user hasn't chosen one, matching internal/web's.
+const defaultBirthdayColor = "#ec4899"
+
+// birthdayWindowPast/birthdayWindowFuture bound how many years around the
+// current one the synthetic Birthdays calendar generates events for.
+// CalDAV clients sync ahead of time (unlike the web view, which only
+// computes the month currently being browsed), so a fixed window is
+// generated upfront instead.
+const birthdayWindowPast = 2
+const birthdayWindowFuture = 8
+
+// birthdayObjIDRe parses an object ID of the form
+// "<book>~<contact-id-without-ext>~<year>.ics" back into its parts.
+var birthdayObjIDRe = regexp.MustCompile(`^([^~]+)~([^~]+)~(\d{4})\.ics$`)
+
+// birthdayObjID builds the stable object ID for contact c's birthday
+// occurrence in year, encoding enough information to regenerate that
+// exact VEVENT on demand in GetCalendarObject.
+func birthdayObjID(c birthdays.Contact, year int) string {
+	base := strings.TrimSuffix(c.ID, path.Ext(c.ID))
+	return fmt.Sprintf("%s~%s~%d.ics", c.Book, base, year)
+}
+
+// birthdaysCalendarMeta returns the caldav.Calendar metadata for
+// username's synthetic Birthdays calendar.
+func (b *Backend) birthdaysCalendarMeta(username string) caldav.Calendar {
+	return caldav.Calendar{
+		Path:                  calHomePath() + birthdaysCalendarName + "/",
+		Name:                  "Birthdays",
+		Description:           "Birthdays computed from your contacts",
+		SupportedComponentSet: []string{"VEVENT"},
+		MaxResourceSize:       64 * 1024,
+	}
+}
+
+// listBirthdayCalendarObjects generates one VEVENT per (contact, year)
+// pair within the fixed rolling window for every contact of username's
+// that has a parseable birthday.
+func (b *Backend) listBirthdayCalendarObjects(username string) ([]caldav.CalendarObject, error) {
+	contacts, err := birthdays.Collect(b.store, b.dbase, username)
+	if err != nil {
+		return nil, fmt.Errorf("collecting birthdays: %w", err)
+	}
+
+	now := time.Now()
+	var objs []caldav.CalendarObject
+	for _, c := range contacts {
+		for year := now.Year() - birthdayWindowPast; year <= now.Year()+birthdayWindowFuture; year++ {
+			obj, ok := b.encodeBirthdayObject(c, year)
+			if !ok {
+				continue
+			}
+			objs = append(objs, *obj)
+		}
+	}
+	return objs, nil
+}
+
+// birthdayCalendarObject regenerates a single VEVENT for the (contact,
+// year) pair encoded in objID.
+func (b *Backend) birthdayCalendarObject(username, objPath, objID string) (*caldav.CalendarObject, error) {
+	m := birthdayObjIDRe.FindStringSubmatch(objID)
+	if m == nil {
+		return nil, webdav.NewHTTPError(http.StatusNotFound, fmt.Errorf("unrecognized birthday object id"))
+	}
+	book, idBase, year := m[1], m[2], m[3]
+	yearNum, err := strconv.Atoi(year)
+	if err != nil {
+		return nil, webdav.NewHTTPError(http.StatusNotFound, fmt.Errorf("invalid year"))
+	}
+
+	contacts, err := birthdays.Collect(b.store, b.dbase, username)
+	if err != nil {
+		return nil, fmt.Errorf("collecting birthdays: %w", err)
+	}
+	for _, c := range contacts {
+		if c.Book != book {
+			continue
+		}
+		if strings.TrimSuffix(c.ID, path.Ext(c.ID)) != idBase {
+			continue
+		}
+		obj, ok := b.encodeBirthdayObject(c, yearNum)
+		if !ok {
+			break
+		}
+		obj.Path = objPath
+		return obj, nil
+	}
+	return nil, webdav.NewHTTPError(http.StatusNotFound, fmt.Errorf("birthday event not found"))
+}
+
+// encodeBirthdayObject builds the all-day VEVENT for contact c's birthday
+// occurrence in year, returning ok=false if that (month, day) combination
+// doesn't exist in year (e.g. Feb 29 in a non-leap year).
+func (b *Backend) encodeBirthdayObject(c birthdays.Contact, year int) (*caldav.CalendarObject, bool) {
+	start, ok := birthdays.OccurrenceDate(c, year, time.UTC)
+	if !ok {
+		return nil, false
+	}
+	end := start.AddDate(0, 0, 1)
+
+	event := ical.NewEvent()
+	uid := birthdayObjID(c, year)
+	event.Props.SetText(ical.PropUID, uid)
+	event.Props.SetText(ical.PropSummary, birthdays.Summary(c, year))
+	event.Props.SetDate(ical.PropDateTimeStart, start)
+	event.Props.SetDate(ical.PropDateTimeEnd, end)
+	event.Props.SetDateTime(ical.PropDateTimeStamp, time.Now().UTC())
+	event.Props.SetText(ical.PropTransparency, "TRANSPARENT")
+
+	cal := ical.NewCalendar()
+	cal.Props.SetText(ical.PropVersion, "2.0")
+	cal.Props.SetText(ical.PropProductID, "-//nidus//birthdays//EN")
+	cal.Children = append(cal.Children, event.Component)
+
+	var buf strings.Builder
+	if err := ical.NewEncoder(&buf).Encode(cal); err != nil {
+		return nil, false
+	}
+
+	objID := birthdayObjID(c, year)
+	return &caldav.CalendarObject{
+		Path:          calObjectPath(birthdaysCalendarName, objID),
+		ModTime:       time.Now(),
+		ContentLength: int64(buf.Len()),
+		ETag:          fmt.Sprintf(`"bday-%s-%d"`, strings.TrimSuffix(c.ID, path.Ext(c.ID)), year),
+		Data:          cal,
+	}, true
+}