You should be using Bowtie 2 instead of bowtie:
Bowtie 1 was released in 2009 and was geared toward aligning the relatively short sequencing reads (up to 25-50 nucleotides) prevalent at the time. Since then, technology has improved both sequencing throughput (more nucleotides produced per sequencer per day) and read length (more nucleotides per read).
In particular, Bowtie 2 supports local alignment, which is essential when mapping microRNA. All microRNA sequences are short, which means that there will be adapter read-through in the sequenced reads. This adapter sequence will not map to the genome, and that will cause global aligners (like Bowtie) to fail.
An alternative approach would be to trim off palindromic adapter sequences prior to aligning (which it is possible you've tried to do given the file name). Because of adapter read through, standard adapter trimming will not be sufficient. What needs to be trimmed off is the reverse-complement of the adapter sequences. I have no experience using fastp, so don't know if it is capable of doing that.
However, even after trimming there will still be some additional short sequences left on some reads, so a local alignment would still be a good idea.
Doing a local alignment with Bowtie 2 is much easier and faster than trying to troubleshoot adapter read-through issues. The command line you would run is similar, but not identical:
bowtie2-build -f miRNA.fa miRNA
bowtie2 --local -x miRNA -1 SRR16643593_1.NEW.trim.fq -2 SRR16643593_2.NEW.trim.fq | samtools sort > test.bam