/** @var MagentoEavApiDataAttributeInterface $attribute */
$attribute->setData('used_in_forms', ['adminhtml_customer']);
$attributeResource->save($attribute);

public function save(MagentoEavApiDataAttributeInterface $attribute)
    {
        try {
            /** @var MagentoEavModelResourceModelEntityAttribute */
            $this->eavResource->save($attribute);
        } catch (Exception $e) {
        ...
    }

use MagentoCustomerApiAddressMetadataInterface;
use MagentoEavApiAttributeRepositoryInterface;
use MagentoEavModelConfig as EavConfig;
use MagentoEavSetupEavSetupFactory;
use MagentoFrameworkSetupModuleDataSetupInterface;
use MagentoFrameworkSetupPatchDataPatchInterface;

....
    /**
     * @param ModuleDataSetupInterface $moduleDataSetup
     * @param EavSetupFactory $eavSetupFactory
     * @param EavConfig $eavConfig
     * @param AttributeRepositoryInterface $attributeRepository
     */
    public function __construct(
        ModuleDataSetupInterface $moduleDataSetup,
        EavSetupFactory $eavSetupFactory,
        EavConfig $eavConfig,
        AttributeRepositoryInterface $attributeRepository
    ) {
        $this->eavSetupFactory = $eavSetupFactory;
        $this->moduleDataSetup = $moduleDataSetup;
        $this->eavConfig = $eavConfig;
        $this->attributeRepository = $attributeRepository;
    }

    /**
     * @inheritdoc
     */
    public function apply()
    {
        /** @var MagentoEavSetupEavSetup $eavSetup */
        $eavSetup = $this->eavSetupFactory->create(['setup' => $this->moduleDataSetup]);

        $attributeCode = 'test_attribute';

        $entityTypeId = AddressMetadataInterface::ENTITY_TYPE_ADDRESS;
        $setId = AddressMetadataInterface::ATTRIBUTE_SET_ID_ADDRESS;
        $eavSetup->addAttribute($entityTypeId, $attributeCode, [
            'type' => 'int',
            'input' => 'boolean',
            'label' => 'Test attribute',
            'required' => 0,
            'user_defined' => 1,
            'default' => 0,
            'system' => 0,
            'position' => 60,
        ]);

        $eavSetup->addAttributeToSet($entityTypeId, $setId, null, $attributeCode);

        $attribute = $this->eavConfig->getAttribute($entityTypeId, $attributeCode);
        $attribute->setData('used_in_forms', [
            'adminhtml_customer_address',
            'customer_address_edit',
            'customer_register_address'
        ]);

        // works. deprecated, I remember
        // $attribute->getResource()->save($attribute);

        // the attribute is saved, but the information on the forms in which the attribute is added is not saved
        $this->attributeRepository->save($attribute);
    }