[time] Fix strftime %Z and %z returning wrong timezone (#15330)

esphome/components/time/posix_tz.cpp

@@ -4,6 +4,7 @@
 
 #include "posix_tz.h"
 #include <cctype>
+#include <cstdio>
 
 namespace esphome::time {
 
@@ -442,6 +443,18 @@ bool parse_posix_tz(const char *tz_string, ParsedTimezone &result) {
   return internal::parse_dst_rule(p, result.dst_end);
 }
 
+// Format a POSIX offset (positive = west) as "+HHMM" / "-HHMM" for display.
+// Convention: negate POSIX sign so east-of-UTC is positive (ISO 8601 / RFC 2822).
+void format_designation(int32_t posix_offset, char *buf, size_t buf_size) {
+  int32_t display = -posix_offset;
+  char sign = display >= 0 ? '+' : '-';
+  if (display < 0)
+    display = -display;
+  int h = display / 3600;
+  int m = (display % 3600) / 60;
+  snprintf(buf, buf_size, "%c%02d%02d", sign, h, m);
+}
+
 bool epoch_to_local_tm(time_t utc_epoch, const ParsedTimezone &tz, struct tm *out_tm) {
   if (!out_tm) {
     return false;

esphome/components/time/posix_tz.h

@@ -36,6 +36,9 @@ struct ParsedTimezone {
   bool has_dst() const { return this->dst_start.type != DSTRuleType::NONE; }
 };
 
+/// Format a POSIX offset as "+HHMM"/"-HHMM" into buf (must be >= 6 bytes).
+void format_designation(int32_t posix_offset, char *buf, size_t buf_size);
+
 /// Parse a POSIX TZ string into a ParsedTimezone struct.
 ///
 /// @deprecated Remove before 2026.9.0 (bridge code for backward compatibility).