Short answer:
If you don't want your habitable worlds to look like object but instead want them to like mere dots in the sky, make them not much more than 6,371 kilometers in diameter (half the the diameter of the Earth) and make their closest approach to each other not much more than 30 million kilometers or 18,641,135 so they can both orbit within the habitable zone of their star.
Long Answer:
I have looked at the moon and not only been able to see it as a disc but also been able to see light and dark areas on its surface. So its angular diameter as seen from Earth of about 30 arc seconds is much more than great enough to be seen as a disc.
And of course the Moon is not an earthlike planet by most standards while Earth is the most Earth-like planet known. Earth has over three times the diameter of the Moon so it would have to be three times as far away as the Moon to appear as small as the moon does from Earth, and several times that to appear like a dot instead of a disc.
The angular diameter of an object with a diameter of d at a distance of D is 206,265 times d/D arc seconds. There are sixty arc seconds in an arc minute and the smallest angular diameter which can be resolved by the unaided human eye is about one arc minute.
In our solar system the planet which is closest in size to Earth and which comes closet to Earth sometimes as they both orbit the Sun is Venus.
Venus has an average radius of 6,051.8 kilometers and thus a diameter of 12,103.6 kilometers. A seen from Earth, Venus looks largest when it is closest to Earth almost directly between the Sun and the Earth, and thus looks like a thin crescent. When Venus is closest to Earth it is about 41 million kilometers or 25 million miles from Earth.
So the angular diameter of Venus when closest to Earth should be 205,625 times 12,103.6 divided by 41,000,000 or205,625 times 0.000295209, or 60.696523 arc seconds. And that is about 1.0099 arc minutes, which is approximately the minimum angular diameter to be seen as an object instead of a mere dot of light.
It is said that people with good vision can sometimes see with the unaided eye Venus when closest to Earth as a crescent shape instead of a dot. I myself have sometimes looked at Venus and thought that I might possibly be seeing it as a very tiny crescent on the edge of visibility.
Assuming that an "Earthlike planet" would have half to twice the diameter of Earth, since the average radius of Earth is 6371 kilometers and its averaged diameter of 12,742 kilometers, an "Earthlike planet" would have a diameter of 6,371 to 25,484 kilometers.
For a planet to have an angular diameter of 1 arc minute or 60 arc seconds, the distance to the planet would have to be 3,437.75 times the diameter of the planet.
So if a planet had a diameter of 6,371 kilometers, it should be at a distance of 3,437.75 times 6,371 kilometers, or 21,901,905.25 kilometers to have an angular diameter of 1 arc minute or 60 arc seconds.
So if a planet had a diameter of 25,484 kilometers, it should be at a distance of 3,437.75 times 25,484 kilometers, or 87,607,621 kilometers to have an angular diameter of 1 arc minute or 60 arc seconds.
So if you desire that when the two Earthlike planets are at their closest their angular diameters should appear to be about 1 arc minute or 60 arc seconds, and that people with human eyesight can just barely detect them as objects instead of mere dots of light. and if the "Earthlike planets" have diameters between 6,371 and 25,484 kilometers, their closest approach should be between 21,901,905.25 and 87,607,621 kilometers.
If you want the two planets to be more easily seen as planets from each other, their closest distances should be closer, and if you want them to never bee seen as objects instead of dots of light, their closest distances should be farther.
Since the two planets will be at their closest when they are lined up with each other and with the Sun, the closest distance between them will be approximately equal to distances between the semi-major axes of their two orbits.
And if you want both the planets to be within the habitable zone of their star, you will want the habitable zone of their star to be wide enough to include both orbits.
There is a simple way to find the inner and out limits of the habitable zone of star. Find the habitable zone of the Sun, and find the ration between the luminosities of that star and the Sun and allow for the inverse square rule.
Here is a link to estimates of the limits of the habitable zone of the Sun made in the last 60 years. Notice how much they vary.
https://en.wikipedia.org/wiki/Habitable_zone#Solar_System_estimates
The estimate by Kasting et al in 1993 is widely used and gives a conservative estimate of 0.95 to 1.37 AU, a difference of 0.42 AU or 62,831,105.69 kilometers. Their optimistic estimate gives limits of 0.84 to 1.67 AU, a difference of 0.83 AU or 124,166,232.7 kilometers.
The estimate by Kopparapu et al in 2013 gives an estimate of 0.99 to 1.67 AU, a difference of 0.68 AU or 101,726,552.1 kilometers.
So the good news is that some estimates of the habitable zone of the Sun give room for two habitable planets to orbit within it at distances where they never look like objects when seen from each other and always look like tiny dots of light.
The bad news is that in order to get the right temperatures for liquid water near the inner and outer edges of their habitable zones, scientists often assume those planets have atmospheres unbreathable for humans to regulate the temperatures.
The only calculation that required an atmosphere breathable for humans was Dole in 1964, with a a range of 0.725 AU to 1.24 AU, and range of 0.515 AU or 77,042,903.41 kilometers. And I suspect the inner edge might be much farther out than Dole calculated.
So I suggest that you make your two habitable Earthlike planets quite small, not much more than half the diameter of Earth, and make their closest approach not more than 30,000,000 kilometers.
