There are many adapter board available for SO8 to PDIP8, mainly because it fits nicely into the PDIP8 footprint, but I couldn’t find anything that meant it was ‘socket compatible’ when you get a DIP16 IC socket. So…
Here is one I designed that uses SMT pin headers and means as long as there is some space around the IC you can use the same pin footprint as a DIP16.

The board overhangs each side of the DIP16 socket by approx 3mm as shown here.
Blue is the bottom layer and red the top.
The “1” designates pin1 on the SO16 IC.

The only other part needed is the SMD pin strips which can be found various places, such as Aliexpress : https://www.aliexpress.com/item/32896209964.html (SMT Type1)
If you need the PCB itself, (and the header strip), we have a few available, just drop us an email or use the Contact page.
Alternatively, the gerber files are available for download.
