Beutepanzer.ru imdicates the capture in running order of about a thousand T26s and 400 BTs. However, at the time, the German forces were convinced of a swift victory, and a lot of commanders were not interested in the additional troubles of trying to man and maintain lots of these additional tanks. By the time that they were disavowed of this line of thinking, the tanks were not entirely viable on the battlefield. plus, being older than T34s etc, they couldn't be run as hard, they were less reliable.

The photographs indicate that a number of the tanks saw service in the police units, much as the captured French tanks ended up doing. For more information, if you can find it, there is a Panzer Tracts specifically on the Beutepanzers, but mine is in he office and I'm on vacation right now.

The number of 15000 tanks seems rather suspect, since according to Dmitriy Shein, the Red Army only had 13981 tanks in Western military districts as of June of 1941. Out of those tanks, 1362 belonged to the 4th repair category (in need of major repairs, requiring a tank factory), 1476 tanks were in the 3rd repair category (in need of medium repairs, requiring service in a regional workshop). Those tanks would be of very little use to the Germans, as it would be incredibly difficult to repair them. The most populous category, 2nd repair category (light repairs, could be carried out by crew), contained 8986 tanks, but a large amount of these tanks were sitting around immobile because of a shortage of spare parts. Shein estimates that as many as 25% of tanks belonging to this category were useless because there were no track links for them. It's likely that the Germans would either not use these tanks at all or use them for a brief period of time until something broke, and then discard them.

Only 2145 tanks belonged to the first category (no need of repairs). Old tanks like the ones you mention made up a fairly small portion of this category. However, now there's the problem of these tanks being vulnerable to literally every anti-tank weapon the Wehrmacht had, plus their gasoline engines made them more vulnerable to burning, making it harder for the Germans to capture them intact.

The easiest way to pick up one of these serviceable obsolete tanks would be if it was abandoned without fuel. However, the Germans were short of fuel themselves, and did not have the luxury of fueling up random junk they found in hopes that it would work. The T-26 was more or less equivalent in combat performance to the Pz35(t), and those were phased out from the Wehrmacht fairly quickly. There was no reason to refurbish and support a large number of these tanks. They would have been put back into action in singular cases like with police units. Baryatinskiy writes that only 100 Soviet tanks of various types were in service with the Wehrmacht by October of 1941.

Sources:

M. Baryatinskiy, Trofeynaya bronetankovaya tekhnika vermakhta

D. Shein, Poryadok v tankovykh voiskah

They did convert them to different uses at some point, and there are many pictures of them

Like this one here where they mounted a Pak 97/38 on a T-26 caption

They removed the turrets of some and used them as prime movers. caption caption

Some of the turrets were used as fixed fortifications caption

They even put one of the T-26 turrets on the chassis of a Renault R35 caption

And some were used on armored trains caption