That is normal in mongosh. The database was dropped, but your database context still exists. The moment you create an object in the database it will be actually created.
If you change db to admin and list the databases you will see that students does not exist. Or you can use the listDatabases command to the same effect. Example of both below:
mongosh 'mongodb://127.6.0.1/students' --quiet
students> db.dropDatabase()
{ ok: 1, dropped: 'students' }
students> db.adminCommand({listDatabases:1}).databases.forEach(x => print(x.name))
admin
config
local
test
students> use admin
switched to db admin
admin> show dbs
admin 40.00 KiB
config 48.00 KiB
local 72.00 KiB
test 72.00 KiB
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