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/birthdays/birthdays.go

@@ -0,0 +1,126 @@
+// Package birthdays computes virtual "birthday events" from a user's own
+// contacts, shared by the web calendar UI (internal/web) and the CalDAV
+// backend (internal/caldav) so both present identical titles/dates for the
+// synthetic Birthdays calendar without duplicating the parsing logic.
+package birthdays
+
+import (
+	"bytes"
+	"fmt"
+	"regexp"
+	"strconv"
+	"strings"
+	"time"
+
+	"github.com/emersion/go-vcard"
+
+	"github.com/yourusername/caldav-server/internal/db"
+	"github.com/yourusername/caldav-server/internal/store"
+)
+
+// Contact holds one contact's parsed birthday.
+type Contact struct {
+	Name  string
+	Book  string
+	ID    string
+	Month time.Month
+	Day   int
+	Year  int // 0 if the vCard's BDAY has no year (e.g. "--08-20")
+}
+
+// fullRe matches a BDAY value that includes a year, in either
+// "YYYY-MM-DD" or the older vCard 3.0 "YYYYMMDD" form.
+var fullRe = regexp.MustCompile(`^(\d{4})-?(\d{2})-?(\d{2})`)
+
+// noYearRe matches a year-less BDAY value per RFC 6350 §4.3.1,
+// "--MM-DD" or "--MMDD".
+var noYearRe = regexp.MustCompile(`^--(\d{2})-?(\d{2})`)
+
+// ParseBirthday extracts month/day (and year, if present) from a vCard
+// BDAY field value. Returns ok=false if v isn't a recognized date format
+// or names an impossible month/day.
+func ParseBirthday(v string) (month time.Month, day int, year int, ok bool) {
+	v = strings.TrimSpace(v)
+	if m := noYearRe.FindStringSubmatch(v); m != nil {
+		mo, _ := strconv.Atoi(m[1])
+		d, _ := strconv.Atoi(m[2])
+		if mo < 1 || mo > 12 || d < 1 || d > 31 {
+			return 0, 0, 0, false
+		}
+		return time.Month(mo), d, 0, true
+	}
+	if m := fullRe.FindStringSubmatch(v); m != nil {
+		y, _ := strconv.Atoi(m[1])
+		mo, _ := strconv.Atoi(m[2])
+		d, _ := strconv.Atoi(m[3])
+		if mo < 1 || mo > 12 || d < 1 || d > 31 {
+			return 0, 0, 0, false
+		}
+		return time.Month(mo), d, y, true
+	}
+	return 0, 0, 0, false
+}
+
+// Collect scans every one of username's own address books for contacts
+// with a parseable BDAY field.
+func Collect(st *store.Store, dbase *db.DB, username string) ([]Contact, error) {
+	books, err := dbase.ListAddressBooks(username)
+	if err != nil {
+		return nil, err
+	}
+
+	var contacts []Contact
+	for _, book := range books {
+		ids, err := st.ListObjects(username, "card-"+book)
+		if err != nil {
+			continue
+		}
+		for _, id := range ids {
+			data, err := st.GetObject(username, "card-"+book, id)
+			if err != nil {
+				continue
+			}
+			card, err := vcard.NewDecoder(bytes.NewReader(data)).Decode()
+			if err != nil {
+				continue
+			}
+			bday := card.PreferredValue(vcard.FieldBirthday)
+			if bday == "" {
+				continue
+			}
+			month, day, year, ok := ParseBirthday(bday)
+			if !ok {
+				continue
+			}
+			name := card.PreferredValue(vcard.FieldFormattedName)
+			if name == "" {
+				name = id
+			}
+			contacts = append(contacts, Contact{
+				Name: name, Book: book, ID: id, Month: month, Day: day, Year: year,
+			})
+		}
+	}
+	return contacts, nil
+}
+
+// OccurrenceDate returns the date c's birthday falls on in year, and false
+// if that combination doesn't exist (e.g. Feb 29 in a non-leap year,
+// where Go's time.Date would otherwise silently normalize to March 1/2).
+func OccurrenceDate(c Contact, year int, loc *time.Location) (time.Time, bool) {
+	occ := time.Date(year, c.Month, c.Day, 0, 0, 0, 0, loc)
+	if occ.Month() != c.Month || occ.Day() != c.Day {
+		return time.Time{}, false
+	}
+	return occ, true
+}
+
+// Summary formats c's virtual event title for the given year:
+// "🎂 Name", or "🎂 Name (Age)" if c's birth year is known.
+func Summary(c Contact, year int) string {
+	s := "🎂 " + c.Name
+	if c.Year > 0 {
+		s += fmt.Sprintf(" (%d)", year-c.Year)
+	}
+	return s
+}