Sorry, what's a "pro shop"?

>A pro shop is a sporting-goods shop within a public or private-membership amateur sporting activities facility of some kind, most commonly a golf course, where it will typically be located in the country club building. In the case of golf pro shops, such stores usually provide equipment such as golf balls, clubs, shoes, and tees, as well as golf-themed gift items, and sometimes snacks or refreshments. Aside from golf courses, pro shops are also frequently found at bowling alleys, pool and snooker halls, tennis and racquetball courts, ice and roller hockey rinks, and football (soccer) facilities.

https://en.wikipedia.org/wiki/Pro_shop

And then you hope they divulge their secrets while shopping for sports equipment?

I imagine it's a good "in" to learn about their social life, which can lead to secrets being divulged. If you know where and how often they play sports, it's probably not terribly hard to arrange for your colleague to bump into them at the golf course (or wherever) and try to strike up a friendship. It's not as if the spy agencies had cellphone GPS logs to track these guys, so the human element was important.

Even asking a regular customer, "Hey, what happened to Ivan? I haven't seen him around. Is he still in the area?" while they're shopping for sports equipment could be a conversation that provides valuable information about someone's whereabouts.

The meaning I know for that is essentially the store and sometimes a bit of a hangout spot associated with a golf course (so named because of the golf professional(s) available there). Not sure if there's other meanings.

Isn't that a golf shop? I didn't know it was popular in Russia.

Golf store that usually offers lessons, swing analysis, club fitting, etc.