How do you guys negotiate your salary when job hunting?

I know that this topic isn’t something easy to talk about in public, but I would like some advice from you guys.

I am working in the pharma sector and my current contract is ending in 6 more months. With no obvious signs of my superiors wanting to convert me to a permanent staff due to budget freeze, work wise having no room to learn more stuff as my colleagues are always busy with work, rumours that they are cutting down manpower, I am job hunting and I hope to do more than what I am currently doing, which is routine testing. (To be frank, anybody can do routine testing, it is just following SOP)

While job hunting, I can’t help but to note that a lot of jobs that I found on Linkedin, mycareersfuture and so on are from 3rd party recruiters, and applications to companies directly through their websites are either in-processing or outright rejected without any interviews. My current salary is around $4.2k, so I feel that it isn’t too much to ask for mid $4k-low $5k for someone that is having ~2years of experience in the pharma sector.

However, from a quick chat with a 3rd party recruiter sourcing for a major company in the pharma sector, I was quite surprised to note that this 3rd party recruiter isn’t willing to match my current pay, saying that my salary (~$4.2k) is too high and if they were to factor 13rd month AWS, variable bonus, transport allowance and so on, it would be too much. (Note that my current contract role doesn’t have any AWS and there is only a tiny amount of transport allowance, contract completion bonus of 0.5 months of my current monthly salary). Another chat with another recruiter recommend me jobs which I need to take a pay cut, which obviously I don’t want and rejected.

How do you guys negotiate your salary when job hunting? Honestly speaking, I don’t have any skills to shout about, except for knowing various testing methods, and I wanted to jump to something within the industry that is not so stagnant, such as R&D or related fields, but having no experience in this field is putting me at a disadvantage compared to other applicants who have advantage in these fields, and there is no formal learning opportunity for me to learn what other departments are doing (such as cross department immersion program, shadowing other departments etc)