In your question, there are two ways we could say the data are being "partitioned", which are:
via repartition, which uses a hash partitioner to distribute the data into a specific number of partitions. If, as in your question, you don't specify a number, the value in spark.sql.shuffle.partitions is used, which has default value 200. A call to .repartition will usually trigger a shuffle, which means the partitions are now spread across your pool of executors.
via partitionBy, which is a method specific to a DataFrameWriter that tells it to partition the data on disk according to a key. This means the data written are split across subdirectories named according to your partition column, e.g. /path/to/parquet/file/DATE=<individual DATE value>. In this example, only rows with a particular DATE value are stored in each DATE= subdirectory.
Given these two uses of the term "partitioning," there are subtle aspects in answering your question. Since you used partitionBy and asked if Spark "maintain's the partitioning", I suspect what you're really curious about is if Spark will do partition pruning, which is a technique used drastically improve the performance of queries that have filters on a partition column. If Spark knows values you seek cannot be in specific subdirectories, it won't waste any time reading those files and hence your query completes much quicker.
If the way you're reading the data isn't partition aware, you'll get a number of partitions something like what's in bsplosion's answer. Spark won't employ partition pruning, and hence you won't get the benefit of Spark automatically ignoring reading certain files to speed things up1.
Fortunately, reading parquet files in Spark that were written with partitionBy is a partition-aware read. Even without a metastore like Hive that tells Spark the files are partitioned on disk, Spark will discover the partitioning automatically. Please see partition discovery in Spark for how this works in parquet.
I recommend testing reading your dataset in spark-shell so that you can easily see the output of .explain, which will let you verify that Spark correctly finds the partitions and can prune out the ones that don't contain data of interest in your query. A nice writeup on this can be found here. In short, if you see PartitionFilters: [], it means that Spark isn't doing any partition pruning. But if you see something like PartitionFilters: [isnotnull(date#3), (date#3 = 2021-01-01)], Spark is only reading in a specific set of DATE partitions, and hence the query execution is usually a lot faster.
1A separate detail is that parquet stores statistics about data in its columns inside of the files themselves. If these statistics can be used to eliminate chunks of data that can't match whatever filtering you're doing, e.g. on DATE, then you'll see some speedup even if the way you read the data isn't partition-aware. This is called predicate pushdown. It works because the files on disk will still contain only specific values of DATE when using .partitionBy. More info can be found here.
/path/to/parquet/file/DATE=*- philantrovert