They wouldn't. Here's how it works:

1) The court would issue a judgement for Twitter, against Musk, for $44b.

2) Musk would either voluntarily pay it by selling his own assets, or he would refuse. If he refuses, then:

3) Twitter would go about seizing and selling Musk's assets, until they have raised funds to cover the $44b judgement.

Twitter could levy whatever brokerage or account Musk uses to hold his shares. Somewhere there is an account which records the shares. Twitter would serve the entity managing the account with a levy, and order the shares be liquidated.

Order the legal entities which possess the shares to transfer ownership of them. Actually keeping track of stocks is complicated but ultimately a boring bureaucracy.

Well, Tesla is a Delaware company[1], so I assume they have some leverage.

1: https://sec.report/CIK/0001318605

Lawyers are lawyers

Contempt of court is independent of the original cases criminal vs civil distinction.

You can have criminal contempt in a civil case and criminal contempt in a civil case. The rules vary by state but in PA it’s civil contempt is used to force people to comply where criminal is punishment for disobedience.

Are you under the impression that judges presiding over civil cases cannot exercise their inherent power (in some jurisdictions) to jail those in (severe) contempt of court?