This is how I would build the flow.
However, if there was a LOT of files/rows and I had access to premium connectors, I'd probably do it differently so as to perform a bulk update to Excel.
See full flow below. I'll go into each of the actions.

Manually trigger a flow is setup similar to yours where the person running the flow can enter the Month.

Get files (properties only) will retrieve all the Excel files. I believe this will only return the first 100 files by default. If you have around 600 then you should change the Top Count to ensure it gets all files. In my example I've set it to 2000.

To create the new Excel file where the combined output will go - I've created an Excel file to use as a Template with the Table and columns already created. This way we can get the content from that blank Excel file and create a new file based on it.
Get file content using path gets the content from the Excel template.

Create file uses the content from our Excel template and appends the Month as part of the file name.

Apply to each file iterates over each of the files.

List rows present in a table retrieves the rows from the current Excel file we are iterating over. I used the Identifier for the current file. Note that I've also set a Top Count here as the List rows present in a table action will only retrieve the first 256 rows by default (I'm not sure how many rows you have in your Excel files). Also note that I've set a filter to only bring back rows for the specified Month.

Apply to each row iterates over each row in the current Excel file.

Add a row into a table adds each of the rows returned into the Excel file we created. Because the Table name is dynamic we need to add the data dynamically. Note that I've also added the Sick and Vacation values for the Total using the add formula. It assumes there is always a value entered for Sick and Vacation, even if just 0.

{
"ID": @{item()?['ID']},
"Month": @{item()?['Month']},
"Sick": @{item()?['Sick']},
"Vacation": @{item()?['Vacation']},
"Total": @{add(float(item()?['Sick']), float(item()?['Vacation']))}
}