A couple things are missing from this discussion .....Number one, is Tamron ALSO makes a 35-150 f2.8 -4 for much less money ! ....the f2-2.8 version is very much a niche lens - as mentioned, for indoor sports/event shooters. If you are outside, the need for f2-2.8 is very questionable. Number two, is Sigma also makes a very good 24-105 Art lens.
As for me, the practicality of a 24-105 would win me over ( I have the Sigma 24-105 Art in A-mount.) - but I have considered and looked at both Tamron versions for my Canon.

It appears you have already made up your mind because of your quote, "finances are a consideration". So I feel you have already made up your mind to get the Tamron.
When I shot Nikon I had a Nikon 24-120 which served me well as a sort of carry "one lens on vacation" mantra.
So when I got my Sony a9 I got the Sony 24-105 on sale from B&H for around $1100. I took it with me on travels to the Panama Canal and to the National Parks in Utah this year. I always use a polarizer for most of my shots.
The f4 was not a problem with todays high iso shooting capabilities. I also have always liked what 24mm does in landscapes.
I have never used the Tamron and cannot comment on it.
However, on B&H 82% of users of the Sony give it a 5, 69% of the users of the Tamron give it a 5.
Of course users ratings should NOT be taken into consideration because what do these people really know about photography, it is just their opinion.
The Sony weights in at 1.46 lbs. the Tamron 1.74 lbs. Again, what does the weight have to do with anything.
Bottom line, the Sony when on sale costs about $1100 compared to the very low price of the Tamron of $639.00. A difference of almost $460.00, and $660.00 when the Sony is not on sale. 50% savings for the Tamron.
So, for me, I would buy the Sony cause it was developed and made specifically for my Sony.
The Tamron company makes their glass to operate on many different camera's.
And yes, the IBIS on the Sony camera's works well with the image stabilization on the lens.
But, because the Tamron is cheaper, I would just like to say, enjoy your new Tamron lens.
Below are some grab shots I took with my Sony, not that it means anything.

The Sony 24-105mm f4 G OSS lens is the #1 selling Sony lens in the world, and for good reasons . I have owned Sony A6500, A7RII, A7RIII, A7III, A9 and currently own A7RIV, A1, A7SIII. I currently have 13 native E-mount lenses covering 10mm to 600mm from Sony, Sigma and Tamron. That includes fast primes like my Sony 24mm f1.4 GM, and my Sony 135mm f1.8 GM, along with several f 2.8 zooms and a f2.8 macro lens.

I shoot all subjects worldwide as a longtime pro, and my Sony 24-105mm f4 G OSS is my most widely used lens of them all. It is super versatile, sharp, fast and quiet focus, and yes that lens' OSS coupled with the cameras' IBIS does allow me to handhold that lens at insanely slow shutter speeds.

That being said, many who have that Tamron 35-150mm f2-2.8 love it for events , wedding coverage and more. As a pro photojournalist for the past 48 + years, I would have loved to have such a lens back in the day.

You will have to live with the size and weight of the Tamron, but if you have the Sony 200-600mm like I do, you are used to heavier lenses.

For me, not having any lens wider than 35mm would give me pause. If you do choose to get the Tamron 35-105mm f2-2.8, I suggest you add the Tamron 17-28mm f2.8 in native E-mount.

Since I have the Tamron 17-28mm f2.8; Sigma Art 24-70mm f2.8 DG DN; Sony 24-105mm f4 G OSS; Sigma Art 85mm f1.4 DG DN and Sony 135mm f1.8 GM among the lenses in my kit, I dont really have the need for the Tamron 35-150mm lens. For you that lens might be an excellent choice.

Here just a few shots i have made with my Sony 24-105mm f4 G OSS lens;

1) This award winning shot was made with my A9 and the Sony 24-105mm lens. A local swimmer dives off a pier into the Caribbean Sea on the Island of Sint Maarten/St. Martin. 24mm, ISO 400, f5.6, 1/2000 sec.

2) This shot was named a Worldwide Photo of the Week by Sony Alpha Photographers in 2020. Environmental Scientist Brook H. in a slot canyon near Upper Antelope Canyon, Navajo Lands, Page, Arizona, USA. Sony A9, Sony 24-105mm lens, 24mm, ISO 400, f4, 1/15 sec handheld, all natural sunlight in the canyon.

3) A Parrot in flight on the Caribbean island of Sint Maarten/St. Martin. Sony A1, Sony 24-105mm lens. 105mm, ISO 1600, f4, 1/2000 sec, all natural light

4-5) Two shots of my nephew and his family for their Xmas card, shot In Flower Mound, Texas a couple of weeks ago. Sony A1, Sony 24-105mm f4 G OSS lens. Shot at various focal lengths, f5.6, 1/250 second, handheld .Three Godox AD200Pro strobes with reflectors and diffusers used to light it all, mixed with the ambient light.

One other aspect of an electronic viewfinder - or optical SLR viewfinder for that matter - is that prior to image stabilization it was an essential point for stabilizing the camera and reducing motion blur. One thing I have noticed with the conversion to digital photography - besides seeing many more women than men using DSLRs - is a loss of proper handholding technique. I have a niece who recently finished a college photography class and I still had to show her the "correct" (old school) method of holding her camera. She has thanked me for that advice, since it has improved the number of her acceptable shots.

First of all, I think you are really asking two questions.

The Electronic View Finder is not the LCD Screen on the back of the camera. The EVF is truly in the location where the optical viewfinder used to be--a small screen in the upper left corner of the back. [See the attached photo.] The internal computer takes a sampling of the actual pixel reads from the sensor and puts them in a jpeg form on the screen that is one-half inch or slightly more in diagonal measure.

On the other hand, the LCD display is the large screen on the back of the camera that may or may not pivot out of the plane of the back of the camera. It is usually in the vicinity off two inches in diagonal measure.

Now to give some responses to your questions. First, I like the EVF because, like the viewfinder in older SLR cameras. it displays what the lens actually sees and not some slightly off-axis picture that rangefinder cameras used to show.

I do agree that LCD screens often show very dim images when one is using a digital camera in bright sunlight. These have gotten better over the years, however, outdoors a photographer probably will want to depend upon the EVF. When one is in a setting where the LCD screen can be used, I like to do so because it frees me and my eyes up to look at the full scene of the picture I am framing instead of the truncated version seen through the viewfinder. So, I can see what my framing will leave out that I wish were in. Then only at the last minute do I have to fully concentrate on the LCD screen.

Just some of my thoughts on your questions. --Richard