Postgresql – Most efficient way to query a date range in Postgresql

I have a table with a timestamp with tz column. I want to perform a count / group by query for rows within a certain date range:

select count(1), url 
from app_pageview 
where viewed_at between '2019-01-01' and '2020-01-01'
group by 2
order by 1 desc 
limit 10;

viewed_at has a btree index applied, but when I view explain... it doesn't appear to be using the index:

postgres=# explain select count(1), url 
from app_pageview 
where viewed_at between '2019-01-01' and '2019-01-31'
group by 2
order by 1 desc 
limit 10;
                                                                                       QUERY PLAN                                                                                        
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
 Limit  (cost=2173025.08..2173025.10 rows=10 width=32)
   ->  Sort  (cost=2173025.08..2173025.33 rows=101 width=32)
         Sort Key: (count(1)) DESC
         ->  Finalize GroupAggregate  (cost=2172997.31..2173022.89 rows=101 width=32)
               Group Key: url
               ->  Gather Merge  (cost=2172997.31..2173020.87 rows=202 width=32)
                     Workers Planned: 2
                     ->  Sort  (cost=2171997.28..2171997.53 rows=101 width=32)
                           Sort Key: url
                           ->  Partial HashAggregate  (cost=2171992.91..2171993.92 rows=101 width=32)
                                 Group Key: url
                                 ->  Parallel Seq Scan on app_pageview  (cost=0.00..2163462.00 rows=1706182 width=24)
                                       Filter: ((viewed_at >= '2019-01-01 00:00:00+00'::timestamp with time zone) AND (viewed_at <= '2019-01-31 00:00:00+00'::timestamp with time zone))
 JIT:
   Functions: 13
   Options: Inlining true, Optimization true, Expressions true, Deforming true
(16 rows)

I have generated ~100M rows of dummy data to test this out.

How can I make it more efficient?

Would storing the viewed_at field as two different fields be any use (date and time)

More details for a smaller query (by honing in on a subset of the rows (where site_id='...')

The dummy data generated was for 1M rows per site_id – with 100 different site_id values. site_id is a btree indexed FK

postgres=# explain select count(1), url from app_pageview where site_id = '14efbc9e-332c-11ea-bbe1-0242ac130002' and  viewed_at > '2019-01-01' and viewed_at < '2019-01-31' group by 2 order by 1 desc limit 10;
                                                                                      QUERY PLAN                                                                                       
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
 Limit  (cost=39877.45..39877.48 rows=10 width=32)
   ->  Sort  (cost=39877.45..39877.71 rows=101 width=32)
         Sort Key: (count(1)) DESC
         ->  Finalize GroupAggregate  (cost=39849.68..39875.27 rows=101 width=32)
               Group Key: url
               ->  Gather Merge  (cost=39849.68..39873.25 rows=202 width=32)
                     Workers Planned: 2
                     ->  Sort  (cost=38849.66..38849.91 rows=101 width=32)
                           Sort Key: url
                           ->  Partial HashAggregate  (cost=38845.29..38846.30 rows=101 width=32)
                                 Group Key: url
                                 ->  Parallel Index Scan using app_pageview_site_id_123e6520 on app_pageview  (cost=0.57..38771.07 rows=14844 width=24)
                                       Index Cond: (site_id = '14efbc9e-332c-11ea-bbe1-0242ac130002'::uuid)
                                       Filter: ((viewed_at > '2019-01-01 00:00:00+00'::timestamp with time zone) AND (viewed_at < '2019-01-31 00:00:00+00'::timestamp with time zone))
(14 rows)

table description:

postgres=# \d+ app_pageview                                                          Table "public.app_pageview"
  Column   |           Type           | Collation | Nullable |                 Default                  | Storage  | Stats target | Description 
-----------+--------------------------+-----------+----------+------------------------------------------+----------+--------------+-------------
 id        | integer                  |           | not null | nextval('app_pageview_id_seq'::regclass) | plain    |              | 
 url       | character varying(200)   |           | not null |                                          | extended |              | 
 referrer  | character varying(256)   |           | not null |                                          | extended |              | 
 viewed_at | timestamp with time zone |           | not null |                                          | plain    |              | 
 site_id   | uuid                     |           | not null |                                          | plain    |              | 
 view_hash | character varying(256)   |           |          |                                          | extended |              | 
 unique    | boolean                  |           | not null |                                          | plain    |              | 
Indexes:
    "app_pageview_pkey" PRIMARY KEY, btree (id)
    "app_pageview_site_id_123e6520" btree (site_id)
    "app_pageview_view_hash_d570ced8" btree (view_hash)
    "app_pageview_view_hash_d570ced8_like" btree (view_hash varchar_pattern_ops)
    "app_pageview_viewed_at_84306743" btree (viewed_at)
    "app_pageview_viewed_at_inverse" btree (viewed_at DESC)
Foreign-key constraints:
    "app_pageview_site_id_123e6520_fk_app_site_id" FOREIGN KEY (site_id) REFERENCES app_site(id) DEFERRABLE INITIALLY DEFERRED
Access method: heap