Having Calendar.app and the Mac's Menu Bar Clock present different time zones

When traveling, I carry an old MacBook Air running Big Sur, and I use the stock macOS Calendar.app. I live in the Pacific Time Zone, and am now traveling in the Central European Time Zone. While traveling, I often view and manage home time zone appointments and dates. So that these entries appear accurately in Calendar, I turn on Time Zone Support in Calendar > Preferences, set to reflect my home time zone. Calendar then displays in my home time zone, as I wish. However, the time and date in the Mac’s Menu Bar clock then reflect the home time and date, not the time and date where I am in a different time zone. I would prefer the Menu Bar to reflect the time and date of my actual physical location, while the displayed calendar shows the time and date in my home time zone. Can this be accomplished in the stock macOS?