Thanks for your question.

As you think about your course of action, it is very important that your identification of crabgrass is correct. It can be confused with quack grass. Crabgrass is an annual whereas quack grass is a perennial. Remedial procedures for quack grass are different from those for crabgrass. Look at the following to see how to distinguish between the two:

https://extension.umn.edu/weeds/quackgrass

https://extension.umn.edu/weeds/crabgrass

https://mastergardener.extension.wisc.edu/files/2016/01/Crabgrass-vs-Quackgrass.pdf

In answering your question, I will proceed on the assumption that your identification of crabgrass is correct. Since crabgrass is an annual, it dies back every fall after producing large numbers of seeds. These seeds germinate in the following spring. Although you currently have areas of turf without crabgrass but adjacent to areas where crabgrass is present, due to wind dispersal of crabgrass seeds last fall the unaffected turf potentially may show the presence of crabgrass this spring. Fertilizers that also control crabgrass do so by preventing the germination of crabgrass seed. This control is generally achieved by the incorporation of pre-emergent herbicides in the fertilizer. For these reasons, I would suggest that fertilizer with crabgrass control be used for your entire yard.  See the following for the various methods by which to control crabgrass:

https://turf.umn.edu/news/spring-preemergent-applications-crabgrass

https://www.gertens.com/learn/preventing-crabgrass-in-your-lawn

https://www.kglandscape.com/when-to-apply-crabgrass-pre-emergent-in-mn

https://yardandgarden.extension.iastate.edu/how-to/how-control-crabgrass

Good luck. Please get back to me if you have any questions. Thanks for consulting us.