dwb's comments are 100% correct, but your subsequent capacity / free space requirements appear to conflict with what you're expecting.
First TimeMachine backup Nov 9 2018 (since I last deleted the backup file as it was too big)
I understand you perceived a need to create more space on the backup volume, but you may have complicated matters with that. If you manually delete TM backup files from the backup volume you run the risk of corrupting the entire backup, making it useless. You might need to completely erase the backup volume to fix it, but hold off on that for now until extracting some TM log excerpts which I'll explain presently.
I have seen the same thing happening on a portable Mac where the Time Machine file just goes on growing and growing on the backup server. But this has not been such a problem as not much is stored on the portable.
That should never happen either. Time Machine will create Local Snapshots only to the extent there's room for them, after which it ceases to create them. They're also purgeable, meaning if you want TM to work you should never manually delete them. If you need to download large files that begin to encroach upon a startup disk's capacity, they're on the chopping block—along with many other files macOS will delete (log files, cache files, etc) in increasingly desperate attempts to ensure a startup volume never becomes hamstrung due to lack of space.
- Apple says Local Snapshots are used only if the source volume has "plenty of free space". My empirical data concluded it will use them until the source reaches 80% capacity, but to my knowledge they don't document that value anywhere.
Although I see manual deletion of local snapshots commonly recommended, I have repeatedly tried and failed to make Time Machine malfunction by deliberately filling a source volume to capacity by manually filling it with random data. That experience, and the fact TM requires Local Snaphots for it to work makes me reluctant to recommend interfering with them.
I have never, ever seen Time Machine fixed by messing with it. I have only seen Time Machine work by leaving it alone. Nevertheless altering or otherwise interfering with TM's normal activity seems to a popular pastime, which only results in breaking it. Hence my recommendation to erase the backup drive and start over.
Extracting Time Machine log activity may or may not yield useful data, but if you are interested those instructions follow below.
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To extract potentially relevant Time Machine activity from log consider using the following shell script:
clear; printf '\e[3J' && log show --predicate 'subsystem == "com.apple.TimeMachine"' --info --last 8h | grep -F 'eMac' | grep -Fv 'etat' | awk -F']' '{print substr($0,1,19), $NF}'
Copy (triple-click to select the entire line) and Paste that line in a Terminal window. The Terminal app is in your Mac's Utilities folder.
It extracts Time Machine activity logged during the previous 8 hours. To change that time period change that value. If Time Machine is running there is no need to interrupt TM to use it. Be advised that log is fairly resource-intensive, and if you are using a portable Mac it will consume a lot of battery power as it runs.
log will need a few moments to extract the Time Machine log data. Wait for it to finish. It is normal for its results to include various "errors" and "failures" and none of them are necessarily an indication of anything wrong.
Copy (Edit > Select All and then Copy) and Paste that Terminal window's contents in a reply to this Discussion. macOS's Unified Logging System is privacy-conscious but if you see anything you consider personal, please omit or obscure it yourself before posting.
Quit the Terminal app when you're finished with it.
