Nothing works when the disk is 100% full, and 95% is almost 100%, so this is not totally unreasonable. Running out of disk space is a Very Bad Thing™ and the disk-based shard allocator is there to protect you from the consequences of that. You can adjust its settings if truly needed, but it's preferable to buy more disk space.
You will need to look at the Elasticsearch logs to find more information about this. If you need help interpreting them, please share them here and we'll do our best.
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