Have you asked a glazier for their opinion and options?

No I haven't, I don't anything about glazier. Will look into it. Thanks.

Find a local glazier and take drawer down for a quote

For a quick fix along your comment about adding wood to cover broken glass. If you located a wooden tray that was the exact size to be placed upside down over the bedside drawer. Like a cap over the drawer. This will give you an idea as to whether that glass/wood concept would work. After receiving a quote for repair from a glazier, I would look at temple and Webster, which have a similar drawer for $269. Purchasing this may be cheaper than repair work. In the mean time tape up the glass to protect the furniture and yourself.

Thank you for your suggestion glaziernis quite expensive, also if I buy from temple and webster, will have to replace both which will cost more than $500, which is again a lot of money.

Lonely way to know is to take it to a local glazier for a quote. These units often get damaged

Wondering if you could get a piece of mirror cut to fit the top until you can get it repaired.

I would replace both with wooden bedsides to complement your bed. The mirror ones will always have finger marks on them and as you have experienced, can be dangerously sharp when broken.

as per bigreader take the draw to a glazier who can arrange for a new mirror to fit /glue to the front of the drawer, could be expensive but cheaper than replacing both side tables, good luck