Can I modernize old sliding doors with new frames
No, the aluminum door frames are designed for specifically sized panes that work with each manufacturer's proprietary glazing strategy. Finding a door frame that would fit your glass would be extremely unlikely; equally unlikely would be that a manufacturer would even supply a door frame by itself. Most aluminum door manufacturers will create custom size units, but trying to get them to fabricate a custom door frame only, to fit your glass, would be highly unlikely and more costly than a complete new unit with the glass.

Also, there is the problem of the surrounding aluminum framework and track, which are designed to work with the original door frame and rollers and would not likely work with a new "modern" door frame.

Also, I suspect that an entirely new unit would actually cost less than what you would end up paying, were you able to find a willing supplier.

Also, if your old glass is not tempered safety glass (older units often are not) it should not be used for a door at all.

An alternative might be to have a wood frame designed and built at a custom door and millwork shop; again, likely to be more $$ than an entire new aluminum unit.