The table pictured here is the result of a differential gene expression (DGE) test. In the table, each row is a gene (labeled with the gene ID and name) and each column (besides the first two) are the results of DGE tests. Each cluster has two sub-columns: L2FC (log2 fold-change) which tells you the average relative expression changes between cells of the cluster vs. others; and p-value, which is how significant the change is.
You can make this table yourself by performing DGE tests for all clusters. You've already done this yourself in your Rpubs script! To make it easier though, so you don't have to manually test each cluster, use the FindAllMarkers function. It will compare each cluster to all other clusters and report the L2FCs and p-values.
However, I recommend using the p_val_adj (adjusted p-value) instead of the p-value. This is due to a problem called multiple testing: you are performing many, many tests (each gene in each cluster is a separate statistical test), and we expect 5% of differentially expressed genes (DEGs) to be DE by random chance. Over something like 100,000 tests, that means you'd expect 5,000 of those to be false positives (which is huge). So p-value is adjusted to account for multiple tests.
Once you filter the DEG table (p-adj<0.05), you can do other downstream analyses to describe what has changed between the conditions. You already have a good start in your Rpub script with the violin plots. Cluster 6 is clearly distinct in terms of those genes' expression levels. You could try to figure out what's special with that cluster. Good luck!