A few things to think about: Are you considering confined or unconfined aquifers? If unconfined, are you considering an arid climate where streams tend to be losing (that is, water from streams tend to move into the ground), or humid climates where streams tend to be gaining (that is, water moves from soil to streams)?

You might look up some case studies in Southern California. An example link is below.

There a few approaches that are sometimes used. 1) Simply using surface water when available, instead of groundwater. 1b) Storing surface water in reservoirs. 2) Constructing infiltration basins and letting water percolate through the soil. 3) Injecting water into aquifers.

In general, the water needs to be clean, especially for injection. (Natural infiltration through soil removes at least some pollutants.) There are many potential pollutants to consider: bacteria, nutrients, pesticides, organic chemicals, and residues from a disinfection process. This may necessitate water treatment or water monitoring.

https://pw.lacounty.gov/wwd/web/documents/LessonsLearnedAquifer.pdf

Attached below is answer I made to similar question about water storage, and some could apply to your interest. Dr. Mangiafico also made most of the points I would concur with.

I certainly am not the first to identify that gullies help remove and lower groundwater tables, so gullies and deeply entrenched channels are anti-water storage. So as mentioned or cited in some of my gully papers, control, stabilization and restoration of gullies can be considered a water storage tool for some ecosystems. Gully plugs with drop inlet was one of the methods that has been used to help store water and sediment. At the other extreme, which I do not recommend supporting for water storage is braided streams, which tend to maintain a high water table and more frequent channel adjustments and flooding.

One might consider some of Dr. David Rosgen‘s channel and stream stabilization and restoration approaches to help restore the natural or at least a stable stream morphology and function.

Maintaining the soil’s ability to take up and store water would be important considerations. Although forests, especially pine forests, have a tendency to use more water than grasslands, forests do help infiltrate and store water, especially in areas with high to extreme rainfall intensities. Forests seldom exhibit any direct overland flow as one indicator of their ability to maintain or improve the soil capacity to absorb, transmit and store water. Organics have been reported to hold or at least delay about 4 times their weight in water. Years back, I heard a presentation by Moshe Cohen where a desert area somewhere in Middle East was restored from no streamflow, to areas with perennial flow through restoring native forest type, in this case I think it was cedars. It is difficult to expect some of these practices to work in every circumstance, as planting pine trees onto a native grassland is likely to lower water yield due primarily to increased evapotranspiration.

It seems also pertinent to know where groundwater recharge, transfer and storage capacity comes from. Much is geology related, but actual identification of critical zones for adjustments in management or land use plans or practices is seldom known in enough detail. Increased use of water level monitoring of wells with transducers or other methods would help inventory and monitor periods of recharge and use that may help improve planning. Connection of groundwater data to rainfall events and streamflow records also may help understanding and modeling.

Many of the problems with dams of various types and sizes come from designing and active management and maintenance issues. Dams designed many decades ago are sometimes forgotten by landowners, or at least not actively maintained and managed by lowering before major flood events that are forecasted much better today. Water storage and management in some instances requires a degree of liability and potential for unforeseen issues in some circumstances. For instance, storage and withdrawals with some frequency in karst terrain could elevate sinkholes or other issues. Due to potential liability and other issues, I would recommend considering a licensed engineer to review and sign off on any moderate to significant projects or plans. As needed, the licensed engineer will consult with hydrogeologist or other professionals if there are areas of expertise that need review.

I would like to add some consequences if not planned carefully. Instream flows are needed to maintain aquatic biota and maintain channel function. Recreation and scenery are other benefits that may deserve public consideration. Most countries are likely to have some water laws or regulations covering this type activity, and certainly there is potential to accomplish some well designed augmentation, but also potential for some deleterious effects to water quality. Inventory, knowledge and understanding of aquifers, recharge zones, hydrogeology, surface and groundwater dependent resources would be important to each specific circumstance or evaluation.

An example of an analysis, and there are probably others.

https://www.usbr.gov/lc/socal/reports/LASGwtraugmentation/AppC.pdf

An excellent proposition. I think it is possible at least theoretically. On a practical front, resource needed may be huge based on the distance from a river to water table underground. I think this is genuinely needed to be explored to find solution to the issue of shrinking and drying wells. Best wishes.

Raise the level of the river bed instead. First, with rock dams about 1/2 meter to one meter high. Then, soil accumulates behind those dams, and raises the water table naturally. And you need to measure and control well pumping in the area also. KSA has a project at https://www.greenprophet.com/2020/08/the-al-baydha-project-how-regenerative-agriculture-revived-green-life-in-a-saudi-arabian-desert/