This looks like a rust. Growth on stems as you are seeing is unusual. Usually the pustules are on leaves, but can be on stems.  See http://ipm.ucanr.edu/PMG/GARDEN/FRUIT/DISEASE/pearrust.html and https://craven.ces.ncsu.edu/2020/05/rust-on-callery-pear/. 

I will send your inquiry on to NCSU's PDIC for their diagnosis.

I just received a response from Charles Hodges, a plant pathologist at NCSU:

Sorry for the delay in getting back to you on the pear problem, but it wasn't a clinic sample and it got lost in my email folder. Anyway the problem appears to be a rust - most likely quince rust caused by Gymnosporangium clavipes. The disease occurs on many members of the rose family, such as apple, pear, quince and hawthorn. Supposedly It only infects only the fruits of apple and pear but may infect both leaves and fruit of quince and hawthorn. This doesn't fit with your case, but I don't know what else it could be. The alternate hosts are Juniperus spp., especially eastern redcedar.

Little damage is done to the pear trees, and chemical control of the fungus in the landscape would not be economical. See link below for more information on the disease.

https://ag.umass.edu/fact-sheets/cedar-quince-rust

Let me know if you have more questions.

Welcome