What I can see of your Craftsman 2.3 it looks very much like my Poulan S25's.
If you don't find a Walbro carb you might nose around looking at pictures and see if the Zama carb on flea bay for a S25 looks like yours. (and yes some of them little Walbro carb's do not accept a kit good) they have internal check valves that are normally not serviceable but you can find them now days) I do not USonic them little diaphragm carbs at first at in heated water in a USonic because it appears that maybe the heated cleaner weakens the check valve. A bad check valve usually causes erratic idling issues. Also it's quite common for the button on replacement diaphragms for walbro's to be of a different type than the one being replaced and the carb won't run correctly. (very easily overlooked) Their are also at least two different sizes (types) of REPLACEMENT check valves for the same carb numbers and you have to see yours before buying at around $10-$12. You can see pictures of the different size types on flea bay and you are rolling the dice because a check valve may not get er going. I would suggest looking towards the clone zama and MAKE sure you do not get the H jet too lean.
I'm not sure what carb is on mine.
I'll monitor this thread and If I get a chance in few days (it's very cold outside right now) and you have not found anything I'll see what ype carb's are one mine. Appears as though they may have used both the Zama and the Walbro's. (flea bay says their clone replacements are Zama's for the S25 but you cannot rely on flea bay for correct info.
Them are really good saws if it's of the S25 inside the block (made back when Poulan made quality saws) and worth the effort to repair even though they do not look like much , easy starting and made for the long haul with just little bit of TLC.
When all is correct they will pull a 16-18 inch bar really good even with a aggressive cut.
I use the aggressive cut semi chisel chains on mine that I can manually sharpenen myself. I do not use the low kick back type chains.
I was about ready to throw the first S25 I seen in the trash few years ago thinking it was just another Poulan, but the guys on this site clued me in as to the S25's quality.