Your grandma's old 5.5" smartphone is larger than a modern 6" smartphone

Smartphone screens are indeed getting larger and larger.
It feels like not too long ago when the Samsung Galaxy S2 Mini had a tiny 3.3" display.

Still, 5-5.5" phones became a standard very quickly and continued to dominate the market until the end of the decade.
Ever since Samsung Galaxy S3 (the standard one, not Mini) was released back in 2012, up until the end of 2010s (iPhone Xr/Xs were released in 2018, and budget phones soon followed).

Although 2020 feels like yesterday, we are almost halfway through 2020s. Therefore most consumers have already upgraded to 'bezel-less' smartphones in the past 5 years or so.

However, some still cling to their old Samsungs Galaxy S7 and Huaweis P10, as they are terrified that modern smartphones are too large for them. After all even "smaller" phones have at least 6" displays. Yet their old 5.5"phones already seem too large to comfortably fit in their hands.

Fortunately, there is no reason to fear modern 6" smartphones. The number of inches represents the size of the display. Not dimensions of the phone itself.
The physical dimensions are what decide if the phone fits in one's hand or not.
And due to massive bezels, older phones are much larger than the screen size alone would suggest.

As you can see, a somewhat modern Xiaomi Mi 9 Special Edition with a 6" display is still much smaller than an older Samsung Galaxy A7 with a 5.59" display.

You can use tools such as GSMArena's 3D compare to visually compare different smartphones.
https://www.gsmarena.com/size-compare-3d.php3
But reading the total physical dimensions from spec sheets is also an option.

6" is considered quite small for a modern smartphone, and many budget options come with 6.7 and 6.8" displays. Those will be much larger than old 5" smartphones.
So it's not like you can just grab the first thing from the store shelve and assure your senior relative that it will be smaller than their old phone.
But there are options, not limited to Xiaomi Mi 9 SE.
Popular budget choices include Pixel 4A and Huawei P30.
In the mid-range, there is the Xperia 10 V and Pixel 7A.
And there are even compact flagships such as Zenfone 10 and Sony Xperia 5 V.