If I get you correctly, you want to identify the 4 HKGs from the novel bacterial genome sequences that you have; what you want to do is homologous BLAST. Check this page https://molbiol-tools.ca/Homology.htm to see if you can get suitable online tools. But I will recommend you use NCBI blast standalone. I don't know of any online tool that will do what you want but you can do it using standalone tools

Md. Amdadul Huq It is not useful to analyse together 16S rRNA and MLST sequences. They have very different taxonomic resolution. I would cite Richard Goldstein (https://www.researchgate.net/post/Is_a_multi-locus_sequence_analysis_MLSA_Housekeeping_gene_a_good_replacement_of_a_16S_rRNA_gene_for_bacterial_strains_identification ) : "16S sequencing will speciate. MLST or MLEE does not differentiate species, rather they differentiate within a species. Beware, MLST only analyzes for neutral housekeeping genes not under diversifying selective pressures, thus misses variability typical of the remaining 99% of the genome."

and one more note: you will not construct bacterial phylogenetic tree based on 4 house keeping genes. It will be phylogenetic tree just for 16S rRNA, gyrB, rpoD and rpoB genes.

It really depends on what genus of bacteria you are working with, and what level of phylogenetic resolution you want. Some bacteria such as Shigella, Escherichia, Salmonella have been extensively studied down to individual clonal outbreak lineages, while other bacteria are mostly represented by uncultured environmental samples with no information about them. The rules for taxonomy and nomenclature of bacteria are also sometimes seemingly confusing. For one example a bacteria that produces botulinum toxin and is isolated and characterized after killing one or more humans will be named as "Clostridium botulinum" while the very same bacteria found in the environment or after killing a duck or any other non-human vertebrate could be named "Clostridium butyricum" or "Clostridium sporogenes".

Most bacterial genomes contain many (I think the average is around 8, not sure what the range is) copies of the 16S rRNA gene, so you could either pick one to represent your genome or maybe make a consensus of all of them. You would then concatenated the other genes together with the 16S sequence and do the same for the other "species" genomes your are interested in. In some cases it might be useful to use phylogenetic methods which permit a different model of evolution for each gene, but for most purposes that type of "data partitioning" is not necessary.

For many bacterial "species" there is a large amount of horizontal gene transfer so it may be interesting to see if each gene individually gives a similar or very different phylogeny.