I think some of the posts concerning residency have been somewhat negatively biased or oversimplified, especially those coming from individuals who practice in a different setting than hospital. I just wanted to share some quick thoughts specific to PGY-1 hospital residency.
I think residency is just a way to jam more experience into a shorter time period. Of course it's not strictly necessary because when you are licensed you are able to independently improve or worsen patient care based on your clinical knowledge and abilities. However it is a good way to tilt the odds in your favor that you will be a benefit to the care team by having more initial support as a pharmacist -- by the advice of preceptors, working in a large teaching hospital with complex patients/a culture of learning, and more feedback from staff regarding polishing your practice from both clinical and "soft skills" perspectives. Having periods of time where a preceptor is double checking some of your work helps people realize when they "don't know what they don't know". However depending on the residency there are many periods of handling tasks independently. I'm sure this varies based on how the residency is set up. In my personal experience I staffed ER, ICU, NICU, psych, surgery, cardiology, and GM with no preceptor (barring occasionally calling someone for help which most employees do in unfamiliar circumstances if they can).
It also helped me with improving efficiency so at my current job I can independently and simultaneously handle clinical, dispensing, and precepting tasks for many more patients and learners than I would have been able to as a new grad (safely). Sometimes I am the only pharmacist managing these tasks for ~40 patients. If someone's individual goal is to work at a small hospital that is not very busy, residency may be less necessary as there would be time to look up many things. Being able to borrow a preceptor's experience, and initially have lower patient loads on the start of a residency rotation allows one to learn more in a short period and hopefully be able to provide more benefit to the care team.
I don't think hospital residency would be very beneficial for most practice settings besides hospital. I also don't think most residency trained pharmacists feel superior to those who did not do a residency, but of course I can't speak for everyone. I do feel after finishing a residency I was proud of the hard work I put in which maybe could come across in a bad light depending on the context? You can probably relate to feeling this way when graduating pharmacy school. I definitely respect non-residency trained colleagues and still come to them with clinical questions. I would consider myself better prepared for a staffing job at the end of PGY-1 residency than someone who only had one year of experience in a hospital. However, personal motivation to learn and stay up with studies/guidelines matters more and more then farther you get away from residency training when comparing to a similar candidate who did not do a residency.
Of course the reduction in pay for a year is a negative. This must be weighed in importance with the benefits of a residency. For me the added experience and improved competitiveness in the job market was absolutely worth it. I would not have been considered for my current job without a residency. For others it may not be worth it. I can't speak toward the value of other types of residencies like community. I worked retail for several years as a tech/intern and I think community residency would have lower value from a clinical standpoint but that is largely speculation.
If you made it this far, thanks for reading!
edit: to reply more specifically to OP I would consider broadening the geographical location of your search if you can, as well as potentially getting licensed in the state ahead of time if you are looking to move. Also having more people read your application materials and thinking critically about who your references are (and if they are the strongest choices) is a good place to start as well. Picking references who have a large network in the area you are applying is helpful!