There are plenty of logistical issues. I'm not sure the Sergeant at Arms even owns handcuffs, much less a place to keep people being held, and I'm sure it would suddenly become a huge scandal - but it would be very interesting.
There is no actual jail on premises.
In 1934, the Senate cited two men for contempt of Congress and sentenced them to 10 days in the DC jail. One, William P. MacCracken, Jr, fought the case in court, eventually losing in the Supreme Court case Jurney v. MacCracken of 1935. He served one night of his sentence in the home of the Senate Sergeant-at-Arms and another in the Willard hotel... I was unable to figure out if he ever actually ended up in the DC jail.
"Sir, this is my guest room, please don't break the window trying to escape or my wife will be the one deputized to recapture you."
Maybe not, but the House and Senate Sergeants-at-Arms jointly supervise the Capitol Police, whose officers I'm sure either can deputize at need. I'm fairly certain that the Capitol Police both have and are intimately familiar with the use of the whole panoply of law enforcement gear.
AIUI, that's true. However, action (and inaction) by the Executive and inaction by Congress, not just recently either, complicates matters.
A pretty good article at Lawfare[0] discusses this at some length.
Also a bill[1] was introduced in the House last June to clarify some of these issues.
Hopefully more attention will be paid to ensuring that Congressional oversight is able to function effectively.
However, one must also guard against politicization of those processes -- but, IMHO, that's less important than making sure the Congress can effectively exercise its oversight role.
[0] https://www.lawfareblog.com/can-congress-fine-federal-offici...
[1] https://lieu.house.gov/media-center/press-releases/rep-lieu-...
A lot of this came up during the investigations prior to the Trump impeachment in the context of forcing witnesses to appear.