How to query features without zooming?

Thank you, however my goal is to find what the purple 臺中市 refers to (not the black one), after right clicking Center Map Here, and then the Where Is This you mentioned, https://www.openstreetmap.org/search?whereami=1&query=24.2069%2C120.7013#map=10/24.2044/120.7095 alas I cannot find out, plus it disappears when zoomed.

If you're asking about what some text on a particular map rendering looks like you'll need to post a screenshot for people to be sure, but assuming that you're talking about the "standard" layer on osm.org there are two candidates:

https://www.openstreetmap.org/node/60655918

(the city, in black)

https://www.openstreetmap.org/relation/2921154

(the admin level 4 area, in purple)

The code to decide what gets shown at what zoom level is a bit convoluted. For admin levels it's https://github.com/gravitystorm/openstreetmap-carto/blob/dd096af4f566eb9c31e50ac447215f68e45b563f/admin.mss#L207 - note that not everything gets shown at every zoom level.

An effective way of finding where a name is used is to search using taginfo, in this case https://taginfo.openstreetmap.org/tags/name=%E8%87%BA%E4%B8%AD%E5%B8%82 finds exactly 2 matches (the ones shown above).

I see. I was relying on the built in https://www.openstreetmap.org/search?query=中區

(OK, let's hope the user knows how to input the words he sees on the map.)

(I suppose the two places, having the same location, were pushed apart by the algorithm, so they could both be visible at the same time.)

Actually, the two places don't have the same location. One is a node, one and area, and the place that Mapnik (the software that decides where to put markers) places the area marker doesn't match the node.