You can check insert size distribution using qualimap which is very easy to use and takes sorted bam/sam as input. It gives you complete mapping statistics along with insert size and its standard deviation. Alternatively, you can use bamstats which also gives detailed mapping stats.
Another option is Alfred. We provide example quality control files for different sequencing assays (DNA-Seq whole-exome, ATAC-Seq, ...) and different sequencing technologies (Illumina, ONT, PacBio) at the companion web application so you can have a look if that's what you are looking for (QC files include the insert size).