I tend to look at the "battle of the Beams" in 1940.
Those systems were not developed in a matter of weeks and those systems only make sense for a "strategic" air force.
While the Luftwaffe was used to support the army (tactical) during army campaigns it did not sit idle on the ground at other times.
We can tend to confuse ideas in translation, The RAF wanted to fight the war in the air
without the army.
The Luftwaffe had as ONE of it's missions the bombing of sources of production/supply to help the army out. They had a number of other missions/tasks.
We can argue for a long long time as to whether that made the Luftwaffe a strategic force or a tactical one or we can accept that the Luftwaffe, while predominantly tactical could and did plan for, equipe for and execute strategic missions.
The RAF was the reverse, it planned for, equipped for and executed long range strategic missions and in 1939-40 not very well, In 1940 it's tactical performance was much worse as it was trying to use those early strategic bombers (being replaced by the Wellington, Whitley and Hamden) as general purpose tactical bombers but without training/experience.
German tactical aircraft of 1939/40 were not burdened with 1000 mile ranges.
The Germans did have, as pointed out, a fair number of bombers that could reach strategic targets, they had the training/doctrine to do so, they had equipement coming on line that would help them do so. The British strategic bombers, even the new large twins, depended on a clear night, a starry sky and luck.
Please look at the number of defence plants the Germans bombed over the summer and fall of 1940. Yes they screwed up with insufficient force size, (everybody did at that point) and truly terrible damage assessment post strike for alloting 2nd and 3rd strikes. They didn't hit those plants/factories by missing beachfront pill boxes.
For the British do not confuse the term "light bomber" with tactical bomber in the 1930s. Once the biplanes started going away (the single engine ones) the "light bombers" like the Battle and Blenheim were intended to perform in the strategic strike role. Sanity did prevail and they were not used on such missions by 1939/40 or at least not after the Wellington with it's two power gun mounts proved incapable of defending itself in 1939.
Things changed very quickly in the 1930s and the capabilities of aircraft also changed.
Old William Green book (correction welcome) says the He 111B-2 in mid 1937 could carry 1653lb(750kg) bomb load 1030 miles and 3307 (1500kg) 565 miles, while the latter could certainly be considered tactical the first was??????
DB 600CG engines if 950hp for take-off and 910hp at 13,120 ft.
Ju 86D with Diesel engines was listed as having a tactical radius of 354 miles with max bomb load but a max range of 932 miles, bomb load not given but with auxiliary fuel tanks range was stretched to 1240 miles. Late 1937/early 1938.
600hp diesel engines?
Everybodies "strategic bombers" were in their infancy (or built in very small numbers) at this time.
We also have to consider who was the enemy. We in the post war era tend to see Britain and Germany as the main opponents but for most of the 1930s France would have been the most important enemy facing Germany, few seeing it collapse so quickly.
France was introducing these in the spring of 1937
They only built about 80 but it was listed as having a range of 1240miles with a 5510lb bomb load. More bombs over shorter distance.
In 1940 they were starting to deliver a version with four Hispano V-12s. A single plane of the later type did bomb Berlin twice in 1940 but that is more along the line of the Doolittle raid than an example of French policy.