I have a web map and I am using Geoserver. The Geotiff files are hosted in Geoserver. At the moment I am uploading the tif files from data_dir directory, however there are many files and larger files, so the disk space will not allow to host so much files. Is there a possibility to connect the data source to a Google drive or other cloud platform?
Yes, but performance will be very poor. You could look at using S3 buckets with the unsupported community Cloud Optimized GeoTIFF (COG) extension, but network latency will always be there.
A better option is to make your imagery smaller if possible - make sure it is tiled and compressed, see Paul Ramsey's blog post GeoTiff Compression for Dummies for more details.