Have you sat down and had a family meeting about this? Keep it very calm and not accusatory. Tell him you are worried about this and want to clear it up. That ds2 has some money missing. I don't think you should assume he is guilty until he has had a chance to explain himself. What does your dad say about it?
I know it's very hard, but try and look at the positives too. At least he came home on Friday, even though it was late. And it was better than staying out until midnight on a week day. Is he staying out late with his gf? If so, there are worst things he could be doing. And buying a necklace for his gf is quite a sweet gesture in a way (don't tell him that) although stealing is absolutely wrong. Keep the positives in mind before condemning him totally.
If it does turn out that he has stolen money then of course he needs to suffer natural consequences. So he has to work to pay his brother back. In the pandemic, that probably means doing household chores at home and maybe for your Dad if you are in a bubble together?
Overall, it's fine to express disappointment and anger, but try and direct that towards his actions and faulty thinking, rather than towards his character. Keep saying that you believe he is a better person than his actions are currently demonstrating. Do you feel sick because you think your own parenting is at fault? If so, try to overcome that feeling and deal directly with the issue. If he is the culprit then he did the "easy" thing - rather than saving up - talk to him about how he made himself feel temporarily good by giving his gf a necklace when in reality:
- his girlfriend wouldn't want a necklace that was bought with stolen money
- he has damaged the trust between you all
- he should be the one protecting his younger brother and standing up for him, not causing him problems
- he may feel good temporarily giving his gf jewellery but deep down he knows it's an empty gesture because no work went in to earning the money for it.
Tell him you love him too much to let him delude himself like this!
I hope the mediation goes well. I don't think you should be asking him to attend. It should be mandatory.