A misperception exists about the capability of 10x binocular to resolve closer double stars. The actual limit is much closer than often believed. The closest double star I have resolved with a 10x binocular is 100 Herculis, which has a separation of only 14.3 arc-seconds.

STF 2280 / 100 Herculis
18h07m +26*06′
5.81/5.84 14.3″ pa 183*

A pleasing double at 10x. Two brilliant blue white stars nestled together but fully resolved with the Canon 10x42L handheld and the Maven 10×56 on the Oberwerk PM1 mount.

A key factor is that the instrument must be mounted (or image stabilized like the Canon 10x42L IS). The handheld, non-IS limit is much wider. Also, seated observing is more effective than standing, because it enables a more relaxed and stationary viewing posture making fine detail more easily seen. Another critical factor is that the double star components must be similar in magnitude – if the primary is much brighter than the secondary the resolution limit is wider. The Herculis 100 secondary is only a few hundredths of a magnitude fainter than the primary, in addition to which they are fifth magnitude stars, pretty much ideal for binoculars. I’m not aware of another star that approaches 100 Herculis in this combination of favorable characteristics.
Here is a stelledoppie list of 29 double stars with magnitudes brighter than 8.0, having a difference in magnitude of less than 0.50 and a declination greater than -30 degrees (which is getting far south from my yard in Kansas). 😉

A Sky Safari skylist can be created from StelleDoppie to import as an observing list. Any of the items closer than 100 Herculis are going to be extremely challenging with a 10x binocular, more likely to be seen as two stars in contact or as an elongated star than distinct stars. But worth a try, anyway. If you’re determined to resolve the closer doubles on this list, it would be wise to have a 20x binocular (like the Oberwerk 20×70 ED Ultra) on standby.

This Sky Safari chart shows a few items from the imported 10x doubles skylist, which are labeled by their Henry Draper (HD) catalog numbers. I observed several of them with 10×50 binoculars on Saturday 22 April 2023. Here are my observing notes.

STF 1122 / HD 61907
07h45m +65*09′
7.78/7.80 sep 14.9″ pa 186*
Physical double star

This double in Camelopardalis is what I started the evening with. Seen as evenly matched white stars. I can just resolve them with 10×50 binoculars, but they are much easier with the Oberwerk 15×70 Ultra. 

STF 1321 / HD 79210
09h14m +52*41′
7.79/7.88 sep 17″ pa 99.5*
Physical double star

Not quite as difficult to resolve at 10x compared with STF 1122 but still challenging. At 10x it appears as a pair of ivory-colored stars, nearly in contact. But with the 15×70 the stars are seen as deep yellow. Maybe apricot. One of the highlights of the evening. Easily found in the Talitha leg of Ursa Major, between two bright field stars (18 and 15 UMa) west of Theta and 26 UMa. Considerably easier to resolve with 12x binoculars compared to 10x, BTW.